# Conference submissions

#### Notes on the approach, methods and results of qualitative research for some classes of dynamic systems

Irina Andreeva 1

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

###### Abstract

The paper reflects both the original investigating methods and strictly proved mathematical conclusions of some fundamental original study of a special and the same time extended set of polynomial dynamic systems. The present work has been conducted based on classical methods of the qualitative theory of dynamic systems and ODE's, which were sufficiently supplemented with especially developed for the tasks of this work fresh research methods and approach. These methods of a precise mathematical research, together with some new attitudes, have to appear useful for future studies of applied dynamic systems with the different orders of polynomial right parts. Considering the fact, that dynamic systems are constantly used among the main instruments of mathematical modeling in all branches of contemporary science and technology, such as the development of systems of artificial intelligence and neural networks, control systems, as well as in theoretical and practical studies of computing and producing systems, in the mathematical modeling of physical, social, ecological and biological processes etc., this research work has high actuality. The main point of this research work is to outline and strictly describe a pattern of phase trajectories belonging to a set of studied polynomial dynamic systems, as well as to to the enlisted and fully investigated different subsets of a main set of them, in terms of the Poincare sphere and Poincare disk, the same time introducing a series of new notions and invented research attitudes.

#### Shared quantum generation of post-selected entangled states using double teleportation

1Instituto Tecnológico de Monterrey, , Mexico
2INSTITUTO TECNOLOGICO Y DE ESTUDIOS SUPERIORES DE MONTERREY, Physics and Mathematics, Mexico

###### Abstract

Quantum resources are being used to reach improved applications in computing, processing, security, and communications. The switching between classical approaches settled by the traditional electronics and computing in favor of quantum ones is an ongoing task. In this work, the generation via post-selection of an entangled resource among three parties is proposed to set a kind of authentication through its characterization coming from a shared agreed processing. Such resource could be used by its entanglement degree as fingerprint in authentication. The robustness and the details of the generation are discussed.

###### Acknowledgements:

Authors would like to acknowledge to Writinglab, Institute of Future Education, both initiatives ofTecnologico de Monterrey, Mexico, in the development and production of this work.

#### Influence of Geogebra on academic performance in differential equations of separable variables in engineering students from Antofagasta-Chile.

Jorge Olivares1 , Elvis Valero2

2Universidad Mayor de San Andrés, matemáticas, Bolivia

###### Abstract

In the next paper. We will show the various Geogebra Applets of differential equations of the separable variables type, which served to know the academic performance of the engineering students of the differential equations course of the University of Antofagasta-Chile, during the year 2021. This work is a continuation and expansion of "Animations and interactive creations in first-order linear differential equations: the case of Geogebra".

#### A Unified Algebraic Framework for Information Processing

Fotios Kasolis1

1University of Wuppertal, Chair of Electromagnetic Theory, Germany

###### Abstract

A systematic examination of data analysis methods reveals that many of these methods are built on a common algebraic structure. More precisely, the resulting algebraic structure contains a set, a binary relation, and a counting system, where the term counting system refers to a mapping from the set of $N\times N$ Boolean matrices to the set of $N$-length vectors, provided that the data sample is of size $N$. Such information tuples are used for obtaining probability mass functions from which various statistics are then computed. Here, after presenting the described framework, some standard data analysis, pattern recognition, and topological inference methods are put in context, while brief computational experiments are employed for illustrating the capacity of the framework and for providing further insights.

###### Acknowledgements:

This work was supported in parts by the Deutsche Forschungsgemeinschaft (DFG) under grant no. CL143/18-1

#### Non-Archimedean -analytical approach to interected scalar quantum fields.

Jaykov2 Foukzon1

1Israel Institute of Technology, math, Israel

###### Abstract

A new non-Archimedean analytical approach to quantum fields is presented, which gives an nowel mathematical foundation for manipulating pointwise-defined quantum fields. In proposed approach, a field operator ϕ(x) is not a standard operator-valued tempered distribution, but a nonclassical operator-valued function [1]-[2]. Then formal expressions containing, e.g., ϕⁿ(x),<ϕⁿ(x)>,etc. can be understood literally, and shown to be well defined as ℝ_{c}^{#}-valued functions. In the free field cases, we show that the Wightman functions are explicitly calculated with the pointwise field, without any regularization, e.g., Wick product. We show that some of physicists' naive expressions of Lagrangian λϕⁿ(x) can be rigorously justified. REFERENCES [1] Jaykov Foukzon, Basic Real Analysis on External Non-Archimedean Field ℝ_{c}^{#}. Basic Complecs Analysis on External Field ℂ_{c}^{}=ℝ_{c}^{#}+iℝ_{c}^{#}. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3989960 [2] Jaykov Foukzon,The Solution of the Invariant Subspace Problem. Part I. Complex Hilbert space. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4039068

#### Implementation of Optimization-based Algorithms for Maximum Power System Observability using Synchronized Measurements

Nikolaos Theodorakatos1 , Miltiadis Lytras2 , Angelos Moschoudis3 , Konstantinos Kantoutsis4

1 National Technical University of Athens (NTUA), School of Electrical and Computer Engineering,, Greece
2The American College of Greece, School of Business and Economics, Deree, Greece
3National Technical University of Athens , School of Electrical and Computer Engineering, Greece
4National Technical University of Athens, School of Electrical and Computer Engineering, Greece

###### Abstract

This paper studies mathematical algorithms for delivery maximum power network observability using synchronized measurements. This problem is an intrinsic extension of the minimization of phasor measurement units (PMUs) by considering the least cost number of these devices around the power network and maximizing the reliability for better performance of power electrical networks. Optimization properties are investigated and used to lie a Βranch-and-Βound algorithm (BBA) jointly with Successive Quadratic Programming and Interior Methods to find optimality. Τo evaluate optimal solutions with maximum measurement redundancy, solution algorithms such as BBA, SQP, IPM are used. The nonlinear algorithms mainly rely on local search procedure as the convergence indicator to optimality, whereas BBA is implemented to build a binary-tree to find an optimal solution. Thus, it is reasonable and necessary to compare nonlinear algorithms with BBA to show their difference and their efficiency convergence properties towards global optimality whereas the maximum observability is preserved. Moreover the polyhedron being constructed for the implementation of the BBA scheme is transformed into a polytope solved by a Semi-Define-Programming approach to find appropriate optimal solutions for further optimization study. Numerical studies show significant improvement about the maximum observability over existing optimization schemes already published in the recent bibliography.

#### Research on Optimization Procedure of PMU Positioning Problem Achieving Maximum Observability Based on Heuristic Algorithms

Nikolaos Theodorakatos1 , Angelos Moschoudis2 , Miltiadis Lytras3 , Konstantinos Kantoutsis4

1 National Technical University of Athens (NTUA), School of Electrical and Computer Engineering,, Greece
2National Technical University of Athens , School of Electrical and Computer Engineering, Greece
3The American College of Greece, School of Business and Economics, Deree, Greece
4National Technical University of Athens, School of Electrical and Computer Engineering, Greece

###### Abstract

The Phasor Measurement Unit (PMU) is a monitoring device capable with high-precision time synchronization that measures magnitudes and phase angle of voltage and current from a specific power network bus. Aiming at achieving the optimal PMU positioning problem (OPP) solving, this study proposes a multi-objective optimization function minimized under a set of 0-1 Boolean observability inequality constraints whereas a binary restriction is satisfied. Genetic algorithms (GAs) in conjunction with a Binary Particle Swarm Optimization (BPSO) are used to solve the multi-objective constraint linear integer program (m-CILP) towards optimality. This GA-PSO probabilistic approach aims simultaneously at minimizing the number of PMUs needed and maximizing the measurement redundancy (MR) index. The success of this heuristic approach is proved by comparing its results with those achieved by a Branch-and-Bound (B&amp;amp;B) algorithm which solves the 0-1 m-CILP towards optimality. The minimization models are tested on standard IEEE power networks to show their applicability regarding this multi-objective optimization making problem. The numerical results derived by the GA-PSO models in MATLAB language show that the optimal solutions with regard to the maximum MR are achieved with efficiency and at the same time minimizing the whole cost in the optimization process.

#### Optimization Algorithm‐based Optimal PMU Placement for Power State Estimation and Fault Observability

Nikolaos Theodorakatos1 , Rohit Babu2 , Miltiadis Lytras3 , Angelos Moschoudis4

1 National Technical University of Athens (NTUA), School of Electrical and Computer Engineering,, Greece
2Lendi Institute of Engineering , Department of Electrical and Electronics Engineering, India
3The American College of Greece, School of Business and Economics, Deree, Greece
4National Technical University of Athens , School of Electrical and Computer Engineering, Greece

###### Abstract

Fault observability is an essential application among intelligent monitoring and outage management system tasks used to understand the self-healing networks, one of the most important characteristics of power systems. Further, the determination of the location of a faulty transmission line in a power grid is a vital topic to facilitate the self-healing network and to maintain the continuity of power supply. Self-healing is an operational aspect of electrical power networks for real-time identification and localization of faulty transmission lines for the whole power network. This paper proposes algorithmic models that determine the optimal number of PMUs and their placement sites to achieve a fault observable system whereas the state-estimation issue is examined. The optimization models discussed herein find a configuration of PMU locations with a least number of devices that locates any fault occurring in a transmission power network. An optimization process is presented within a nonlinear programming model coupling a synchronized phasor as well as conventional measurements. As a comparative reference, a zero-one integer linear program is used that satisfies global optimality. Metaheuristic algorithms such as a binary-particle swarm optimization and genetic algorithm have been employed to determine a fault observable power system. The algorithm models are illustrated with an IEEE-14 bus system. Simulation results are tested on different size power systems to verify the efficacy of the proposed algorithmic approach. The presented results are promising given that they are in complete agreement with those found by the zero-one integer linear programming model.

#### Study of the stability for three-dimensional states of dynamic equilibrium of the electron Vlasov-Poisson gas

Yuriy Gubarev1 , Yang Liu2

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

###### Abstract

The Vlasov-Poisson model of boundless collisionless electron gas in self-consistent electric field continues to be one of the basic models for a number of modern physics areas, such as particle physics, electrodynamics, plasma physics, etc. This is due to simplicity, clarity, and obvious effectiveness of the model in describing complicated processes of the micro world. For example, the Vlasov-Poisson model is successfully used for development and operation of accelerators with colliding beams, which make it possible to accelerate elementary particles additionally by means of hot electron gas. Despite the fact that this model has been intensively studied for a long time, from the point of view of the mathematical stability theory, it was possible to establish only sufficient conditions for the theoretical stability (at semi-infinite time intervals) of a number of dynamic equilibrium states with respect to both small and finite perturbations, but from some incomplete unclosed subclasses. In this report, we consider spatial motions of boundless collisionless electron Vlasov-Poisson gas in three-dimensional Cartesian coordinate system: $$\frac{\partial f}{\partial t} + v_i\frac{\partial f}{\partial x_i} + \frac{\partial \varphi }{\partial x_i}\frac{\partial f}{\partial v_i} = 0,$$ $$\frac{\partial ^2\varphi }{\partial x^2_i} = 4\pi \int \limits _{\mathbb{R}^3}f({\bf x}, {\bf v}, t)d{\bf v}; (1)$$ $$i = 1, 2, 3; f = f({\bf x}, {\bf v}, t) \geq 0; f({\bf x}, {\bf v}, 0) = f_0({\bf x}, {\bf v}).$$ Here $f$ denotes the distribution function of electrons (for reasons of convenience, their charges and masses are assumed to be equal to unity); $t$ is time; ${\bf x} = (x_1, x_2, x_3)$ and ${\bf v} = (v_1, v_2, v_3)$ denote coordinates and velocities of electrons; $\varphi ({\bf x}, t)$ is the potential of self-consistent electric field; $f_0({\bf x}, {\bf v})$ denotes the initial data for function $f$. We suppose that the distribution function $f$ asymptotically approaches zero as $|{\bf v}| \rightarrow \infty$, and this function along with the potential $\varphi$ are periodic in argument ${\bf x}$ or asymptotically approach zero as $|{\bf x}| \rightarrow \infty$ too. It is assumed that the mixed problem (1) has the following exact stationary solutions: $$f = f^0({\bf x}, {\bf v}) \geq 0, \varphi = \varphi ^0({\bf x});$$ $$v_i\frac{\partial f^0}{\partial x_i} = - \frac{\partial \varphi ^0}{\partial x_i}\frac{\partial f^0}{\partial v_i}, (2)$$ $$\frac{\partial ^2\varphi ^0}{\partial x^2_i} = 4\pi \int \limits _{\mathbb{R}^3}f^0({\bf x}, {\bf v})d{\bf v}.$$ The aim of this report is to prove the absolute linear instability for the spatial states of dynamic equilibrium (2) of boundless collisionless electron Vlasov-Poisson gas with respect to small three-dimensional perturbations $f^\prime ({\bf x}, {\bf v}, t)$ and $\varphi ^\prime ({\bf x}, t)$: $$\frac{\partial f^\prime }{\partial t} + v_i\frac{\partial f^\prime }{\partial x_i} + \frac{\partial \varphi ^\prime }{\partial x_i}\frac{\partial f^0}{\partial v_i} + \frac{\partial \varphi ^0}{\partial x_i}\frac{\partial f^\prime }{\partial v_i} = 0,$$ $$\frac{\partial ^2\varphi ^\prime }{\partial x^2_i} = 4\pi \int \limits _{\mathbb{R}^3}f^\prime ({\bf x}, {\bf v}, t)d{\bf v}; (3)$$ $$f^\prime ({\bf x}, {\bf v}, 0) = f_0^\prime ({\bf x}, {\bf v}),$$ where $f_0^\prime ({\bf x}, {\bf v})$ denotes the initial data for function $f^\prime$. In the report, a transition from kinetic equations (1) which describe the spatial motions of electron gas under study to an infinite system of relations similar to the equations of isentropic flow of a compressible fluid medium in the “vortex shallow water” and the Boussinesq's approximations was carried out. In the course of instability proof, the well-known sufficient Newcomb-Gardner-Rosenbluth condition for stability of dynamic equilibrium states (2) with respect to one incomplete unclosed subclass of small spatial perturbations was conversed. Also, some linear ordinary differential second-order inequality with constant coefficients was obtained for the Lyapunov functional. An a priori exponential lower estimate for growth of small three-dimensional perturbations (3) follows from this inequality when the sufficient conditions for linear practical instability of the considered dynamic equilibrium states found in this report are satisfied. Since the obtained estimate was deduced without any additional restrictions on the dynamic equilibrium states under study, then the absolute linear instability of the spatial states (2) of dynamic equilibrium of boundless collisionless electron Vlasov-Poisson gas with respect to small three-dimensional perturbations (3) was thereby proved. The report results are fully consistent with the classical Earnshaw instability theorem from electrostatics. At present, the area of applicability for the Earnshaw theorem is expanded from electrostatics to kinetics, namely, to the boundless collisionless electron Vlasov-Poisson gas. Finally, constructiveness is inherent in the sufficient conditions for linear practical instability established here, which allows them to be used as a testing and control mechanism for conducting physical experiments and performing numerical calculations. In particular, these conditions can be applied to solve the problem of additional acceleration for elementary particles by electron plasma clumps. Specifically, they must be performed during the formation of a bunch of electrons. Due to this, it will take less time to create an electronic clot. On the contrary, after the electron cluster has formed, the conditions should not be fulfilled. Then the electronic clot will last longer. Thus, there is a real opportunity to control the acceleration of elementary particles with the help of electron plasma clumps.

###### Acknowledgements:

This work was supported partially by China Scholarship Council.

#### The Mathematical, Reading, and Scientific Literacies for Sustainable Development in the Fourth Industrial Revolution

Vincent Theodore Balo1 , Angeline Pogoy2 , Michel Plaisent3 , Prosper Bernard4

1Cebu Normal University, , Philippines
2Cebu Normal University, , Philippines
3Universite du Quebec a Montreal , Department of Management, Canada
4Universite du Quebec a Montreal, , Canada

###### Abstract

Technology has radically changed the global landscape as it affects the way people communicate, learn, and think. In the onset of the fourth industrial revolution, many are inspired to find the formula in becoming a global player in this revolution. Hence, this study was intended to explore the explanatory and prediction factors for global players in the fourth industrial revolution. The main data set used was the PISA 2018 results of the seventy-seven (77) participating countries along with the Reading, Mathematics, and Science areas. Data mining binary logistic regression were utilized. Results revealed that the global players of the fourth industrial revolution are generally performing above the average in Reading, Mathematics, and Science as opposed to the non-global players, the odds of a country to become a global player in the industrial revolution are higher to those who are performing well in the three PISA areas, and the country can be predicted to become a global player if they are highly inclined in Science but less in Reading. The study concluded that the global players in the current industrial revolution considered reading, mathematical, and scientific literacies dire important. But they treated reading as essential and fundamental literacy for them to develop other literacies most especially the scientific literacy. Scientific literate citizens drive the whole country to scientific discoveries and technological glories, which make them stand apart from the rest of the world.

#### Unifying Approach to a Solution of Linear Systems of Equations $\mathbf{Ax=b}$ and $\mathbf{Ax=0}$: Outer Product Application and Angular Conditionality

Vaclav Skala1

1University of West Bohemia, DEpt. of Computer Science and Engineering, Czech Republic

###### Abstract

A solution of linear systems of equations $\mathbf{Ax=b}$ and $\mathbf{Ax=0}$ is the key part of many computational packages. This paper present a novel formulation based on the projective extension of the Euclidean space using the outer product (extended cross-product). This enables to solve the both cases, i.e. $\mathbf{Ax=b}$ and $\mathbf{Ax=0}$. The proposed approach actually leads actually to an "analytical" solution of linear systems in the form $\bm{\xi}=\bm{\alpha}_1 \wedge \bm{\alpha}_2 \wedge \ldots \wedge \bm{\alpha}_n,$ on which the other vector operation can be applied before using the numerical evaluation. This contribution also proposes a new approach to the conditionality estimation of matrices applicable also to non-squared matrices. It splits the conditionality to "structural" conditionality showing matrix property if nearly unlimited precision is used, "numerical" issue which depends on numerical representation with respect to the right-hand side influence, if given.

#### A Quintuple Integral containing the Hermite Polynomial $H_n(x)$ and a Generalized Logarithmic Function: derivation and evaluation

Robert Reynolds1

1York University, Mathematics and Statistics, Canada

###### Abstract

In this paper we derive a new multidimensional definite integral whose kernel involves the Hermite polynomial $H_n(x)$. This definite will be used to derive a theorem in terms of a closed form solution represented by the Hurwitz-Lerch zeta function. Special cases are evaluated in terms of fundamental constants. All the results in this work are new.

###### Acknowledgements:

We wish to acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC).

#### Fluorescence characteristics analysis of rodamine B

Yongzhong Ma1

1Engineering University of PAP, School of Equipment Management & Support, China

###### Abstract

In this paper, the fluorescence characteristics of rodamine B essence under different concentration, different solvent, different PH and different excitation time were studied, and the influence of these factors on the fluorescence spectrum of rodamine B essence was analyzed. The results showed that when the concentration of basic rose essence was less than 1×10-4g/L, the fluorescence intensity was positively correlated with the concentration. When the concentration of basic rose essence was greater than 4×10-3g/L, the fluorescence intensity increased first and then decreased with the increase of basic rose essence. When the dielectric constant of the solvent increases, the fluorescence intensity of the solution increases. When PH is 1 ~ 2, the fluorescence intensity increases gradually. At 3, the fluorescence intensity remained unchanged.

#### Simulation analysis of explosive power of a detonation bomb

Yongzhong Ma1

1Engineering University of PAP, School of Equipment Management & Support, China

###### Abstract

In order to analyze the safety of detonation bomb, an explosion simulation model of the bomb was established based on LS-DYNA simulation platform, the fragmentation distribution and velocity variation were analyzed, and the killing radius of the bomb was evaluated. The results show that the fragmentation size of the projectile is unevenly distributed, and the large-mass low-speed fragment generated in the middle of the explosive is the main source of killing, with a killing radius of about 2.33m. This study provides a scientific basis for the development and application of small high-light detonation bomb, and also provides a useful reference for the research and design of similar ammunition.

#### Nonlinear Dynamics Transmission Error Analysis of a two-stage gear system with gear flexibility and high load

Chao Li1

1Jiangsu Automation Research Institute, Department of Computer, China

###### Abstract

A non-linear dynamic model of a 14-DOF (degree of freedom) two-stage spur gear with time-varying stiffness and flexible gears is developed for the practical problem of non-linear disturbances in a two-stage spur gear system of a model space drive mechanism, the validity of which is demonstrated by motion simulation experiments. The dynamic characteristics of this gear system are analysed. Tooth shape modifications of the two-stage gear pair are compared. The variation of dynamic load coefficients and load transfer errors for different modification parameters is analysed. In this paper, tooth profile errors are enhanced in the dynamic model. The effect of tooth profile error and variable load torque on transmission error is analysed. With a linear modification, a modified length of 0.6mm and a tooth profile modification of 0.004mm is the best modification solution, with a 36% reduction in the peak and valley values of the load transfer error. The study of the non-linear dynamics model of a two-stage spur gear and the transmission error of high load loads is enriched, providing an important reference for the practical design of gear systems.

#### Fast Neutron Detector Simulation

Olga Sidorova1

1Joint Institute for Nuclear Research, Laboratory of Neutron Physics, Russia

###### Abstract

PFN emission of 235U(n,f) reaction are under investigation in JINR for last 20 year. The recent achievements in experimental apparatus simulation are the subject of this presentation. The object of simulation is prompt fission neutron (PFN) detector used for resonance neutron induced fission of U-235. The neutron source was IREN facility and double ionization chamber (DIC) with Frisch grids was used for fission fragment spectroscopy. The PFN detector was multi detector system consisted of 32 BC501 scintillation liquid filled modules from the Sionix (Netherlands) company. Detectors were located on the sphere surface with 50 cm radius. Double Frisch gridded ionization chamber, used as fission spectrometer at the same time generated trigger signal for PFN registration apparatus. For each fission event the following simulated information was recorded: correlated fission fragments time mark, emission angle in respect to the selected coordinate frames along with the pulse heights and shapes of neutron detector signals. Multiple neutron scattering and the cross-talks were taken into account in order to evaluate contribution of those effects in the final results.

#### PFN multiplicity study in resonance neutron induced fission of U-235

Shakir Zeynalov1

1JINR, FLNP, Russia

###### Abstract

Investigations of prompt fission neutron emission are important in understanding the fission process in the sharing of excitation energy among the fission fragments. Experimental activities at JINR on prompt fission neutron (PFN) emission are underway for more than 20 years. Main focus lied on investigations of prompt neutron emission from the reactions 252Cf (sf) and 235U(n,f) [2-10] in the region of the resolved resonances. Resonance neutron energy region is interesting in the testing of nuclear scission model []. For the 235U(n,f) reaction strong fluctuations of fission fragment mass and the mean total kinetic energy distributions have been observed as a function of incident neutron energy [16, 37]. In addition fluctuations of prompt neutron multiplicities were also observed in [44]. The goal of the present study is to verify the current knowledge of prompt neutron multiplicity fluctuations and study the correlations with fission fragment properties. Recent measurement of PFN multiplicity in resonance neutron induced fission of 235U(n,f) reaction [27] reveal surprising result, stimulated us to investigate the PFN multiplicity at IREN with new high efficiency experimental setup.

#### Prompt fission neutrons investigation at IREN in resonance neutron energy range

Shakir Zeynalov1 , Olga Sidorova2

1JINR, FLNP, Russia
2Joint Institute for Nuclear Research, Laboratory of Neutron Physics, Russia

###### Abstract

Autors: Shakir Zeynalov1 and Olga Sidorova1,2 1JINR, Frank Laboratory of Neutron Physics, Dubna, Moscow region,141980 2Dubna State University, Dubna, Moscow region Investigations of prompt fission neutron emission are important in understanding the fission process in the sharing of excitation energy among the fission fragments. Experimental activities at JINR on prompt fission neutron (PFN) emission are underway for more than 20 years. Main focus lied on investigations of prompt neutron emission from the reactions 252Cf (sf) and 235U(n,f) [2-10] in the region of the resolved resonances. Resonance neutron energy region is interesting in the testing of nuclear scission model []. For the 235U(n,f) reaction strong fluctuations of fission fragment mass and the mean total kinetic energy distributions have been observed as a function of incident neutron energy [16, 37]. In addition fluctuations of prompt neutron multiplicities were also observed in [44]. The goal of the present study is to verify the current knowledge of prompt neutron multiplicity fluctuations and study the correlations with fission fragment properties. Recent measurement of PFN multiplicity in resonance neutron induced fission of 235U(n,f) reaction [27] reveal surprising result, stimulated us to investigate the PFN multiplicity at IREN with new high efficiency experimental setup.

#### Temperature extremes and slow trends: effect on resource competition ecosystems

Ivan Sudakow1 , Dubrava Kirievskaya2 , Ekaterina Cherniavskaia3

1University of Dayton, Physics, United States
2University of Dayton, Geology, United States
3AARI, Oceanography, Russian Federation

###### Abstract

We consider a simple model of a resource competition ecosystem. We investigate as that ecosystem biodiversity evolves under temperature changes, which could include slow climate trends, extreme phenomena, and a combination of those both effects. The model also includes the formation of new species. We show that slow trends can lead to total species extinctions, but if new species appear at a sufficiently large rate then biodiversity conserves, or, at least extinction rate diminishes. Extreme phenomena essentially increase the extinction rate. In the most sophisticated model, where temperature oscillations are determined by a random dynamical system with a strange attractor, we can observe a catastrophic bifurcation when the growth of temperature oscillations leads to a sharp increase in the extinction rate.

#### MATHEMATICAL MODELLING OF THE DISTRIBUTION NETWORK FOR THREE-PHASE POWER FLOW ANALYSIS

Samson Ayanlade1 , Abdulrasaq Jimoh2 , Emmanuel Ogunwole3 , Abdulsamad Jimoh4 , Sunday Ezekiel5

1Lead City University, Electrical and Electronic Engineering, Nigeria
2Obafemi Awolowo University, Electronic and Electrical Engineering, Nigeria
3Cape Peninsula University of Technology , Electrical, Electronic and Computer Engineering, South Africa
4University of Ilorin, Electrical and Electronic Engineering, Nigeria
5Olabisi Onabanjo University, Electrical and Electronic Engineering, Nigeria

###### Abstract

The status of a power network, as well as the techniques for estimating it, are important in assessing the power network’s operation and control, as well as determining its future expansion. Power flow analysis, which estimates the magnitudes of the bus voltages as well as the power flowing through the system’s lines, may be utilized to identify the state of any distribution network. Power flow analysis of distribution networks necessitates proper mathematical modeling of network components, particularly distribution lines. Typically, single-phase mathematical modeling is used. However, because this mathematical modeling does not reflect the underlying features of the distribution networks, the power flow calculations are insufficiently accurate. In this study, three-phase mathematical modeling was used to analyze the power flow of a practical Nigerian distribution network, and the results were compared to those of a single-phase equivalent. Modified Carson’s equations were used to accurately model the lines of the three phases while accounting for mutual inductances between the phases to compute the line impedances. Thereafter, the three-phase bus admittance matrix of the network under study was developed. The three-phase power flow equations of the distribution network were formulated in the phase frame. The Newton-Raphson power flow technique was adopted to solve the network three-phase power flow problems formulated. A MATLAB program was developed to implement the method. The results revealed that the voltage magnitudes, as well as the active and reactive power losses, were not equal in all the three phases. This contradicts the results of the power flow simulation using single-phase mathematical modeling. Therefore, three-phase power flow analysis better matched the actual distribution network operating circumstances than single-phase power flow analysis.

#### Stability investigation for three-dimensional states of dynamic equilibrium of two-component Vlasov-Poisson plasma

Yuriy Gubarev1 , Jingyue Luo2

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

###### Abstract

In the electrostatic approximation, when the electric field of electrons and ions is self-consistent, the plasma dynamics is described by the kinetic Vlasov-Poisson equations. In this case, such equations are used to study the collisionless motion of electrons, which interact with each other through the Coulomb repulsive forces, against the background of a homogeneous distribution of ions in the whole physical continuum. In three-dimensional statement, the mathematical model for the two-component Vlasov-Poisson plasma is written in the form: $$\begin{array}{c} f_{t}+\vec{v} \nabla_{\vec{x}} f-\nabla_{\vec{x}} \varphi \nabla_{\vec{v}} f=0 \end{array}$$ $$\Delta_{\vec{x}} \varphi=4 \pi(1- \int \limits_{\Re^{3}} f(\vec{x}, \vec{v}, t) d \vec{v}) \quad (1)$$ $$\begin{array}{c} f=f(\vec{x}, \vec{v}, t) \geq 0 ; \quad f(\vec{x}, \vec{v}, 0)=f_{0}(\vec{x}, \vec{v}) \end{array}$$ Here $f$ is the distribution function of electrons; $t$ is time; $\vec{x}, \vec{v}$ are electron coordinates and velocities; $\varphi$ is the potential of self-consistent electric field; $\pi$ is the known constant value; $\Re^{3}$ is physical space or continuum of velocities; $f_{0}$ - the initial data. It is assumed that $f$ and $\varphi$ are the smooth functions, and the integral from the right side of the Poisson equation exists. The mathematical model (1) of a boundless electrically neutral collisionless fully ionized plasma of electrons and ions in the electrostatic approximation (the two-component Vlasov-Poisson plasma) is considered further in index form: $$\begin{array}{c} \frac{\partial f}{\partial t}+{v}_{i}\frac{\partial f}{\partial x_{i}} -\frac{\partial \varphi}{\partial x_{i}}\frac{\partial f}{\partial {v}_{i}}=0 \end{array}$$ $$\frac{\partial^2 \varphi}{\partial x^2_{i}} =4 \pi(1- \int \limits_{\Re^{3}} f(x_i, v_i, t)d\vec{v}) \quad (2)$$ $$\begin{array}{c} f=f(x_i, v_i, t) \geq 0 ; \quad f(x_i, v_i, 0)=f_{0}(x_i, v_i) \end{array}$$ where $\vec{v} = (v_1, v_2, v_3), \vec{x} = (x_1, x_2, x_3), d\vec{v} = d v_1 d v_2 d v_3; i = 1, 2, 3$. The mathematical model (2) of the two-component Vlasov-Poisson plasma has the following exact stationary solutions: $$f=f^0(x_i, v_i), \quad \varphi = \varphi ^0(x_i) \quad (3)$$ $${v}_{i}\frac{\partial f^0}{\partial x_{i}} =\frac{\partial \varphi^0}{\partial x_{i}}\frac{\partial f^0}{\partial {v}_{i}}, \quad \frac{\partial^2 \varphi^0}{\partial x^2_{i}} =4 \pi(1- \int \limits_{\Re^{3}} f^0(x_i, v_i) d v_1 d v_2 d v_3)$$ The aim of this research is to prove the absolute instability for exact stationary solutions (3) to the mathematical model (2) by the direct Lyapunov method with respect to small three-dimensional perturbations. The results of the study are important for solving the problem of controlled thermonuclear fusion. To achieve this goal, the hydrodynamic substitution of independent variables is performed so that the Vlasov-Poisson equations (2) are transformed to the previously known infinite system of three-dimensional equations similar to the equations of isentropic flows of a compressible fluid medium in the vortex shallow water and the Boussinesq approximations. The new defining equations have exact stationary solutions that are equivalent to exact stationary solutions (3). Then these defining equations are linearized in the vicinity of their stationary solutions. A priori exponential estimate from below is constructed for a subclass of small three-dimensional perturbations of exact stationary solutions to the new defining equations, which grow over time and are described by the field of Lagrangian displacements. Since the estimate is obtained for any exact stationary solutions, it proves precisely the absolute linear instability of the latter regarding three-dimensional perturbations. Thus, the Newcomb-Gardner-Rosenbluth sufficient condition $$\begin{array}{c} \frac{d f^{0}}{d\left(\frac{\vec{v}^{2}}{2}+\varphi^{0}\right)} \leq 0 \end{array}$$ for linear stability of exact stationary solutions (3) is reversed and its formal character is revealed. Also, the sufficient conditions for linear practical instability of exact stationary solutions (3) to the mathematical model (2) are found and their constructive nature is discovered. At last, the results of this research are consistent with the well-known Earnshaw theorem on instability in electrostatics and extend the scope of its applicability from classical mechanics to statistical one. As for the significance of these results, they can be used to study the adequacy of mathematical models for plasma to the physical phenomena which the models describe. Furthermore, the results obtained here can be applied to the development and subsequent operation of devices designed to perform the controlled thermonuclear fusion. In order for a plasma confinement device to operate reliably, it needs for us to ensure the practical stability of its dynamic equilibrium states with respect to all acceptable perturbations. In particular, these equilibrium states should be robust in a practical sense for small three-dimensional perturbations. This can be achieved by creation of numerical and physical models, which correspond to the linearized initial-boundary value problem under investigation, with control the sufficient conditions for linear practical instability at some reference time points. In constructing these models, the main focus should be on ensuring that the sufficient conditions for linear practical instability are not met at the expense of those or other known external influences on small three-dimensional perturbations growing with time (for example, by virtue of violation of initial conditions). In consequence, the operation reliability of the device for plasma confinement in working mode will be guaranteed.

###### Acknowledgements:

This work was supported partially by China Scholarship Council.

#### A simple derivation for teaching the tunneling effect through n-sequential barriers

Cristia Vacacela Gomez1

1Istituto Nazionale di Fisica Nucleare , Laboratori Nazionali di Frascati, Italy

###### Abstract

Quantum tunneling (QT), at first approximation, is a microscopic phenomenon where a particle can penetrate and pass through a potential barrier, which is assumed to be higher than the kinetic energy of the particle. This effect, non-predicted by the laws of classical mechanics, plays an essential role in different physical phenomena, such as nuclear fusion in stars, radioactive decay, quantum biology, cold emission, tunnel junction, quantum-dot cellular automata, tunnel diode, tunnel field-effect transistor, quantum conductivity, kinetic isotope effect, scanning tunneling microscope, and more recently, water quantum tunneling. With this in mind and based on the relevant solutions to the Schrodinger equation, we present a simple derivation of one-dimensional quantum tunneling through 𝑛-successive potential barriers, separated by intermediate free and non-free regions. In particular, we show that the transmission coefficient depends strictly on the number (𝑛) of barriers. This finding has never been discussed previously and can be used in future experiments. Our results are expected to be of immediate help for students and educators.

###### Acknowledgements:

The authors would like to thank Corporación Ecuatoriana para el Desarrollo de la Investigación y Academia - CEDIA for the financial support given to the present research, development, and innovation work through its CEPRA program, especially for the “Proyecto 18-Tecnologias Inmersivas” fund.

#### Finite Element Method for Modelling Real Leaves Surface

Osama Ogilat1

1Al-Ahliyya Amman University, Basic sciences, Jordan

###### Abstract

In this article, a novel technique depends on Fitting the Clough-Tocher approach (CT) and the multiquadric radial basis function (RBF) associated through a linear polynomial (RBFL) is applied to recreate three-dimensional leaf surface from the data. Since modeling leaf surface is essential for improving plant model, the exactness of the solution is established by applying the Clough-Tocher multiquadric radial basis function enhanced with a linear polynomial approach (CTRBFL) to real 3D leaf data. It is shown that the (CTRBFL) method generates an exact representation of the leaf surface.

#### Uncovering the geometry of protein interaction network: the case of SARS-CoV-2 protein interactome

Paola Lecca1

1Free University of Bozen-Bolzano, Faculty of Computer Science, Italy

###### Abstract

In most mathematical models and their practical applications, a network represented by a graph is a finite metric space where distance is defined by the number of edges of the shortest path between two nodes. However, as recent studies are already stating, this is not the only geometry of a network [1, 2, 3]. There is in fact the geometry of the latent metric space underlying the organisation of the network structure and the geometry of the metric space induced by the network dynamics [1]. Often, in modelling processes, one geometry is imposed on the network, without considering that the network may have a different one defined by the properties of the nodes and edges representing, respectively the actors and the relationships between actors involved in the physical processes of which the network is a model. It is therefore of great importance to be able to uncover the real geometry of a network and then build a realistic model of its static and dynamic properties based on this real geometry. With this motivation, I present a method to determine the latent geometry of a network and the geometry induced by its dynamics. There are countless benefits that knowledge of network geometry can have in the biological and medical fields. Such networks underlie several biochemical processes, molecular dynamics, and signal generation. These include the understanding of the molecular mechanisms underlying biological processes and the identification of drug targets. I show the practical applications of this research on protein interaction map of SARS-Cov-2 based on previous studies [4, 5]. [1] Boguñá M., Bonamassa I., De Domenico M. et al. Network geometry. Nat Rev Phys 3, 114–135 (2021). https://doi.org/10.1038/s42254-020-00264-4 [2] Mulder D., Bianconi, G. Network Geometry and Complexity. J Stat Phys 173, 783–805 (2018). https://doi.org/10.1007/s10955-018-2115-9 [3] Fernanda S. Tonin, Helena H. Borba, Antonio M. Mendes, Astrid Wiens, Fernando Fernandez-Llimos, Roberto Pontarolo, Description of network meta-analysis geometry: A metrics design study, PLoS ONE, 14(2): e0212650, 2019, https://doi.org/10.1371/journal.pone.0212650 [4] Lecca P. , Carpentieri B., Sylos Labini P., Vella F., Troiani E., Cavezzi A., Analysis of SARS-CoV-2 protein interactome map, IEEE International Conference on Bioinformatics and Biomedicine (BIBM 2021) - Workshop on Integrative Data Analysis in Systems Biology (IDASB 2021), 9-12 December 2021 - Virtual online conference, pp. 2429-2436, doi: https://doi.org/10.1109/BIBM52615.2021.9669641 [5] Gordon D.E., Jang G.M., Bouhaddou M. et al. A SARS-CoV-2 protein interaction map reveals targets for drug repurposing. Nature 583, 459–468 (2020). https://doi.org/10.1038/s41586-020-2286-9

###### Acknowledgements:

This study is supported by the project SABLE (Computational methods to simulate the SARS-CoV-2 attack to red blood cells), RTD 2021 nr. 5744, funded by the Free University of Bozen-Bolzano, Italy.

#### Modeling and Simulation of Heat Propagation Processes in the Five-Layer Detection Pixel of Thermoelectric Single-Photon Detector

Armen Kuzanyan1 , Astghik Kuzanyan2 , Vahan Nikoghosyan3

1Institute for Physical Research, National Academy of Sciences of Armenia, Material Science Lab., Armenia
2Institute for Physical Research, National Academy of Science of Armenia, Material science , Armenia
3Institute for Physical Research, National Academy of Sciences of Armenia, , Armenia

###### Abstract

We present the results of modeling of heat propagation processes in the $SiO_2/W/FeSb_2/W/Al_2O_3$ five-layer detection pixel of thermoelectric single-photon detector after absorption of one photon, simultaneous absorption of more than one photon, as well as photons absorption with optical delay in the definite or given by the random number generator areas. We have considered the absorption of photons with an energy of 0.95 eV in the detection pixel with a surface area of $10 × 10 μm^2$ and various thicknesses of the antireflection layer ($SiO_2$), absorber ($W$), thermoelectric sensor ($FeSb_2$), heat sink ($W$), and substrate ($Al_2O_3$). The three-dimensional matrix method for partial differential equations was used in calculations. The cases of simultaneous absorption of several photons on a length of 1 μm of the absorber surface as well as absorption of photons following with optical delay 30 – 5 fs are investigated. It is shown that the decay time of the detector signal to the background substantially depends on the number of simultaneously absorbed photons; therefore, the number of absorbed photons up to eight photons can be determined. $SiO_2/W/FeSb_2/W/Al_2O_3$ detection pixel can also detect photons with optical delay of 5 fs, which corresponds to the count rate of $2×10^{14}$ Hz. The five-layer detection pixel of the thermoelectric single-photon detector with $FeSb_2$ sensor can also detect photons absorbed with an optical delay of 5 fs independently of photons absorption areas location in the absorber. A detector with such characteristics is highly demanded in many fields of quantum electronics.

###### Acknowledgements:

The authors are grateful to A.M. Gulian for his interest in the work and useful discussions. This work was supported by the Science Committee of RA, in the frames of the research project №21T-1C088 “Sensor development of the thermoelectric single-photon detector for UV radiation taking into account thermal noise”.

#### Comparative validation of sub-grid scale models with converging zero/non-zero value in the laminar flow using Reynolds number dependence of an unsteady turbulence field

Naoyuki Iwata1 , Hiroki Suzuki2 , Shinsuke Mochizuki3

1Yamaguchi University, Graduate School of Sciences and Technology for Innovation, Japan
2Okayama University, Graduate School of Natural Science and Technology, Japan
3Yamaguchi University, Graduate School of Sciences and Technology for Innovation, Japan

###### Abstract

This study presents a numerical analysis of SGS model validation using the Reynolds number dependence of unsteady turbulence fields. The Smagorinsky model, a typical SGS model for large-eddy simulation (LES), usually needs to be corrected for a value of the model constant in wall turbulence. To examine the necessity of reducing the model constant value of the Smagorinsky model in the low Reynolds number region observed near the wall of the unsteady flow field, a comparison was performed with other SGS models without the need for model constant value correction. As a result, the Smagorinsky model was found to be effective in the low Reynolds number region. For this unsteady turbulence, the period and amplitude of the external forcing term were changed as computational conditions. Also, the Reynolds number was changed to examine the present analysis. In addition, the Reynolds number was changed to verify the current analysis. This analysis showed little difference among the models, regardless of Reynolds number, period, or amplitude. This result suggests that there is little need to correct the model constant values for the Smagorinsky model in unsteady homogeneous turbulent flow fields in the low Reynolds number region.

#### LES analysis on the impact of isotropically reduced spatial resolution of viscous terms on an anisotropic homogeneous turbulence field

Riku Hirabayashi1 , Hiroki Suzuki2 , Shinsuke Mochizuki3

1Yamaguchi University, Graduate School of Sciences and Technology for Innovation, Japan
2Okayama University, Graduate School of Natural Science and Technology, Japan
3Yamaguchi University, Graduate School of Sciences and Technology for Innovation, Japan

###### Abstract

This study presents the effects of reduced spatial resolution in an anisotropic turbulence field. Here, this turbulence field is set to be stationary. We use the implicit large-eddy simulation (ILES) without sub-grid scale (SGS) stresses and LES with the Smagorinsky model to analyse this turbulent field. The convective terms were discretized with second- or fourth-order central difference schemes, and the viscous terms were discretized with second-, fourth-, sixth-, and eighth-order central difference schemes to examine the accuracy of the spatial resolution. The effects of the reduced spatial resolution were examined using the Reynolds number dependence of the turbulence statistics. We have seen that the effects of decreasing spatial resolution depend more on the viscous terms than on the convective terms. When the viscous terms have second-order accuracy, the effects on spatial resolution are more apparent. Small-scale turbulent fields appeared to be significantly affected by the spatial resolution at low Reynolds number conditions.

#### Unifying Matter, Energy and Consciousness

Mahendra Samarawickrama1

1University of Technology Sydney, Computer Science, Australia

###### Abstract

We modelled consciousness to explain how it interfaces with the brain and interacts with matter and energy. As per the mode, consciousness is a fundamental law of nature and life or reality. Regardless of the brain’s massive parallel-processing capability, consciousness has been defined as a high-speed sequential process that leads to awareness. Like time, consciousness is also subjected to relativity. When the observer is moving, both time and consciousness dilate, which does not give an advantage to the moving observer to enhance the awareness over the resting observer. Further, electromagnetic energy of consciousness follows quantum principles and wave-particle duality, which interplays with matter and energy. The rest mass of the consciousness particle increases when increasing the consciousness frequency or decreasing the speed of the consciousness particle. This interplay of consciousness with matter and energy makes consciousness and reality interrelate and follows determinism, realism, and physicalism, the fundamental essences of modern physics. Further, that explains the limitations of the five senses of an observer (i.e., sight, hearing, taste, touch and smell) and the role of consciousness in understanding reality. In future, we would like to extend this model to explain dark matter and dark energy.

#### Statistical insight about students’ perception of teaching performance patterns across the COVID-19 confinement in Engineering programs of Higher Education

1INSTITUTO TECNOLOGICO Y DE ESTUDIOS SUPERIORES DE MONTERREY, Physics and Mathematics, Mexico
2Tecnologico de Monterrey, Mechtronics Engineering, Mexico

###### Abstract

COVID-19 confinement has shaken the educative system with deep changes in teaching, discipline, persistence, and new learning horizons. Student evaluation for instructors in Higher Education is applied as a feedback assessment to improve Education. Such instruments have been applied consistently for decades. Those instruments are commonly paired with other insights to evaluate the learning and teaching impact of teaching innovation or other innovation interventions. Extracting Patterns from Students’ Evaluations of Instructors is a very recurrent practice in university assessments. Commonly based on Likert scales, their analysis to get conclusive findings have been criticized because such gathering techniques fail to exhibit a real ordered and metric scale. Recently, analysis based on statistical data mining and machine learning has led to the construction of new approaches to better understand those scales for such a concrete application. In this work, we explore such techniques based on several joint statistics to analyze the crossing of COVID-19 confinement (from pre-COVID to New Normal) extracting certain student patterns through such period. We propose a joint statistical dashboard to interpret the outcomes for several cohorts crossing the pandemic confinement and transitions from face-to-face to virtual education, and again to face-to-face education.

#### A method for constructing a hierarchy in systems with fuzzy relationships

1 Georgian Technical University, Computational Mathematics, Georgia

###### Abstract

The objective of this paper is to introduce a new method for constructing a hierarchical structuring in systems with fuzzy relationships between elements. The expediency of creating the proposed method is substantiated. The appropriate theoretical basement of the offered method is laid out in the lattice of binary fuzzy relations. The requirements are formulated for the implementation of the process of hierarchical structuring. A key theorem is proved that defines the structural units and types of fuzzy connections between them at each hierarchical level. A detailed practical example, accompanied by graphic illustrations, is given to demonstrate the work of the proposed method. Possible prospects for the development of this direction are outlined.

#### The gravitational mass of the rarefied cloud of the relativistic massive particles

1Joint Stock Company "D.V. Efremov Institute of Electrophysical Apparatus", Scientific Technical Center "Sintez", Russian Federation

###### Abstract

A cloud of relativistic material particles is considered, the gravitational interaction between which can be neglected. The gravitational mass of the cloud is determined for the region where it can be considered as a point body. The dependence of this mass on complete elliptic integral of the 2nd kind on the ratio of the particle velocity to the speed of light is established.

#### Crack Behaviour in Materials: A Comparative Study

1Universiti Malaya, Mathematics, Malaysia

###### Abstract

Crack difficulties are important research topics for multiferroic composite media, which offer a lot of potential for producing multifunctional devices. It is put into consideration the magneto-electro-thermo-elastic coupling effect. The two crack surfaces are symmetrically loaded by a combination of homogeneous thermal, magnetic, electric, and mechanical loadings. Only the shallower region of a deep flaw in the wall structure inside the skin-depth layer impacts the initial temperature Induction Thermography (IT) response while assessing ferromagnetic constructions, but the deeper part has zero influence. This paper provides an exhaustive overview of these crack behavior studies as well as proposes a course of action for future exploration. Based on the literature, three types of crack behavior, which are magnetoelastic, ferromagnetic, and piezoelectric (PE), were explored significantly. Literature reviews have indicated that the magnetoelastic crack studied is popular among researchers around the world. Besides, the procedure and conditions are easier and faster compared to ferromagnetic and PE. Future research should therefore concentrate on the investigation effects of the magnetoelastic crack.

#### Texture segmentation of 3D X-Ray micro-computed tomography images using U-NET

Mohamed Jouini1 , Rashad Heggi 2 , Naser Al-Khalayaleh 3 , Fawaz Hjouj4

1Khalifa University , Mathematics, United Arab Emirates
2Khalifa University , Mathematics, United Arab Emirates
3Khalifa University , Mathematics, United Arab Emirates
4Khalifa University, Math, United Arab Emirates

###### Abstract

Recent advances in numerical methods combined with the use of 3D X-ray micro computed tomography acquisition systems improved the characterization of reservoir rocks at pore scale. This approach, known as digital rock physics (DRP), consists on simulating rock properties using 3D X-ray micro computed tomography images at pore scale. DRP has been extensively used to estimate numerically rock properties like porosity and permeability. This methodology was successful in sandstone reservoir rocks due to their relative homogeneity. Nevertheless, this approach failed in many cases when applied for carbonate reservoirs due to their heterogeneity at several length scales. In order to overcome this limitation, we propose to use the texture information in the images to identify and segment the most representative textural regions. Indeed, several studies showed that texture information is correlated to variations of physical rock properties. In recent years, the advancements made in deep learning algorithms improved largely the performance of segmentation methods. In particular, we focus on a machine learning method based on convolutional neural network called the U-NET architecture to segment 3D X-Ray micro computed tomography images in terms of textures. The challenge is to identify precisely representative textures in highly heterogeneous rocks such as carbonate rocks. We investigate the performance of the proposed segmentation method on both synthetic and real data.

###### Acknowledgements:

The authors would like to thank Abu Dhabi Department of Education and Knowledge (ADEK) in United Arab Emirates for funding the project under grant number EX2018-024. Acknowledgments:

#### Prediction of Plant Allergenic Proteins: machine learning classification approach

Miroslava Nedyalkova1

1unify, chemistry , Switzerland

###### Abstract

The presented perspective comes to the line for building and exploring the allergenic nature of food proteins. The general application of the contribution was to propose a new way of arising the way of understanding in the light of machine learning (supervised and unsupervised) method predicting the allergenic plant proteins. To strategy was based on scoring the descriptors regarding testing the descriptors for calssification and the partitioning procedure based on K-means. The K-nearest neighbor (KNN) classifier was used. The 5-fold cross-validation approach was used to validate KNN classifier in the variable selection step and final classifier. The necessity of developing a robust and valuable method can be set out as efficient to overcome the problem with allergenisity.

###### Acknowledgements:

This work was supported in part by the Bulgarian Science Found - (grant number: K-06- KO /17 - 16.12.2020.)

#### Temporal spectrum of scattered electromagnetic waves in the equatorial ionosphere

Giorgi Jandieri1

1Georgian Technical Uiversity, Internationa Space Agency Georgian Society, Georgia

###### Abstract

Statistical characteristics of the temporal spectrum of scattered ordinary and extraordinary electromagnetic waves in the equatorial region of the terrestrial ionosphere are investigated using the stochastic transport equation for frequency fluctuations applying the ray-(optics) method. Currently equatorial ionosphere is of great interest. Statistical characteristics of scattered electromagnetic waves in this region were not considered till now. Ionospheric conductivity is one of the main properties of the ionosphere which plays an important role in the ionospheric transport mechanism and in the propagation of wave sent from the Earth to ionosphere. The conductivity plays a key role in the dynamics of plasma in the ionosphere and irregularities have different spatial scales usually elongating in the direction of an external magnetic field. Refractive index for the equatorial region has been obtained for the first time. Statistical moments (broadening of the spectrum and shift of its maximum) are analyzed analytically and numerically using the experimental data. The obtained results contain anisotropic factors of elongated electron density irregularities, velocity of a plasma stream, temporal pulsations of the plasmonic structures and inclination angle of electron density irregularities with respect to the geomagnetic lines of force. Investigations of space-time fluctuations of electromagnetic waves radiation are of essential interest for radio astronomy and atmospheric physics. These fluctuations are a disturbing factor at ground-based astronomic observations.

###### Acknowledgements:

This work is supported by Shota Rustaveli National Science Foundation of Georgia (SRNSFG), grant NRF-21-316 "Investigation of the statistical characteristics of scattered electromagnetic waves in the terrestrial atmosphere and application"

#### Model $P(ɸ)_4$ Quantum Field Theory. A Nonstandard Approach Based on Pointwise-Defined Free Quantum fields

Jaykov Foukzon1

1 Israel Institution of Technology, Haifa, Israel., Center for Mathematical Sciences,, Israel

###### Abstract

A new non-Archimedean analytical approach to quantum fields is presented, which gives an nowel mathematical foundation for manipulating pointwise-defined quantum fields. In proposed approach, a field operator ϕ(x) is not a standard tempered operator- valued distribution, but a nonclassical operator-valued function [1]-[2]. Then formal expressions containing, e.g., ϕⁿ(x),<ϕⁿ(x)>,etc. can be understood literally, and shown to be well defined as {∗}^ℝ_{с}^{#}-valued functions. In the free field cases, we show that the Wightman functions are explicitly calculated with the pointwise field, without any regularization, e.g., Wick product. We show that some of physicists' naive expressions of Lagrangian λϕⁿ(x) can be rigorously justified. REFERENCES [1] Jaykov Foukzon, Basic Real Analysis on External Non-Archimedean Field ℝ_{c}^{#}. Basic Complecs Analysis on External Field ℂ_{c}^{#}=ℝ_{c}^{#}+iℝ_{c}^{#}. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3989960 [2] Jaykov Foukzon,The Solution of the Invariant Subspace Problem. Part I. Complex Hilbert space. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4039068

#### FTIR and LRS of 2NH3-thiosemicarbazon and quantum-chemical analysis

Sergo Gotoshia1

1Ivane Javachishvili Tbilisi State University, R. Aglaze Institute of Inorganic Chemistry and Electroqemistry , Laser Center, Georgia

###### Abstract

Thiosemicarbazon (TSC) is known as one the of active complex-productive ligands with different metals. TSC and its derivatives are known as antibacterial, antiviral, antifunginal, antinevrological, biologically active compounds. The complex-productivity ability of TSC with transition metals enhances their pharmacological activity . We have recorded the IR spectrum of 2NH3-thiosemicarbazon on the Fourier IR spectrometer Varian 660 and The Raman spectrum – on the homemade Raman-system, with the excitation wavelength 632.8 nm. For quantum-chemical computations the semi-empirical program MOPAC 8 Ultra has been used. On the basis of theory AM1 the geometrical parameters of optimized molecular structures- bound lengths and angles have been computed. Also the theoretical spectrum and normal frequencies have been computed. The experimental and theoretical data are in satisfactory fit.

#### Tensor Representation of Quadrupole Expansion for Softened Potentials in N-body Simulations

Eraldo Marinho1

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

###### Abstract

A tensor representation for quadrupole expansion is proposed as a recipe for n-body simulations of collisionless stellar systems that do not perform the direct summation method, as is the case of TREECODE. The quadrupole expansion is almost straightforward in the non-softened case, but it is pretty complicated when some softening artifice modifies the potential. A shorthand formula of quadrupole correction for potential and gravity force is derived that can be easily adapted to computer codes like C and FORTRAN. A test is performed to show how relevant it is to incorporate quadrupole correction in n-body codes like TREECODE and particle-mesh methods.

#### Structural health monitoring of tall buildings: the case of Enel Skyscrape

Giorgio Frunzio1

1Università degli Studi della Campania Luigi Vanvitelli, Architecture and Industrial Design, Italy

###### Abstract

The analysis of flaws in structures is an important engineering problem. The identification technique can be a useful tool to develop predictive models that easily allow detecting defects and unexpected problems. Many studies have been carried out to obtain the parameters to represent the behaviour of structures in terms of time histories, frequency, response curves, and mode shapes. The use of simple models based on experimental data is a need to prevent the occurrence of undesired phenomena. In this paper, a method for the structural identification of tall buildings is presented. The method has been applied to the Enel skyscraper situated in Naples, Italy. The 120 meters building is made by the composition of two towers linked on the top by a steel girder with reinforced concrete piled foundations. The identification of this particular reinforced concrete structure has been based on the experimental data obtained by a scaled model. The simplified method proposed consists of a procedure of steps of system identification using a finite element model. An iterative process has been performed updating step by step the model, starting from the first three experimental natural frequencies and modes. The comparison between analytical and experimental results is finally shown.

###### Acknowledgements:

The authors gratefully acknowledge the University of Campania financial contribute and professors Michela Monaco and Antonio Gesualdo for their helpful conversations and support.

#### The influence of the local dynamics in the phase synchronization of a network of a Hindmarsh-Rose neurons.

Emanuel Cambraia1

1Universidade Federal do Paraná, Physics, Brazil

###### Abstract

In this work we study the phenomenon of phase synchronization of a network composed of Hindmarsh-Rose neuron. We show how the individual dynamics of the neurons (periodic or chaotic) affects the phase synchronization process of the network, when the coupling parameter is varied. We show that the synchronization process is a function of the individual neuron dynamics, regardless the network topology. To do so, we construct a bi-dimensional parameter space where the individual dynamics of the neurons may be periodic or chaotic. We notice three regions of interest: the first one, where the individual action potential of the neurons is chaotic and depicts burst regime; the second one, where the dynamics is periodic and depicts burst regime; and a third one, where the neuron dynamics is periodic but depicting spiky regime. For chaotic neurons, the synchronization rote as the coupling parameter grows, shows a monotonic transition, characterized as the large the coupling, the large the synchronization level. When the action potentials of neurons are periodic, the dynamics depicts phase locking for small coupling, leading to a phase synchronized network. As the coupling increases a desyncronization process first occurs, followed by the traditional synchronization rote as the coupling increases. That characterizes a non-monotonic transition to phase synchronization of the network, where two very distinct thresholds of synchronization occur. Finally, a case in which the action potential of neurons is periodic in a spike regime. For this case, a small coupling promotes chaotic dynamics before any phase locking process take place. In this case, again, an almost monotonic transition to synchronization takes place as the coupling parameter is increased.

#### Holomorphic representation of Olshanetsky-Perelomov operators associated with the Weyl group of type Bn

Ibrahim Nonkané1 , Frederic Y2 , Latévi Lawson3 , ALIDA ZINSOU4

1Université THOMAS SANKARA, Département d'Economie et de Mathématiques appliquées, IUFIC, Burkina Faso
2Institut des Sciences et Technologies, Ecole Normale Supérieure, Mathématiques, Burkina Faso
3African Institute for Mathematical Sciences (AIMS) Ghana, Department of Mathematics, Ghana
4Université THOMAS SANKARA, IUFIC, Burkina Faso

###### Abstract

In this paper, we study the holomorphic representation of Olshanetsky-Perelomov operators associated with the weyl group W of type $B_n$. Thus, we view the algebra $\mathcal{H}(\mathbb{C}^n)$ of holomorphic functions as a module over the ring D of invariant differential operators under the group W. Then, we study the holomorphic representation of $\mathcal{D}$. Using the representation theory of the Weyl group W, we construct the irreducible components of $\mathcal{H}(\mathbb{C}^n)$, by explicity providing their generators.

#### Mathematical Modelling of Dendritic Complexity Mechanism in Alzheimer's Disease

RASHMI KUMARI1

1BENNETT UNIVERSITY TIMES OF INDIA GROUP GREATER NOIDA , INDIA, SCHOOL OF COMPUTER SCIENCE ENGINEERING & TECHNOLOGY (SCSET), India

###### Abstract

Alzheimer's disease (AD) is a neurological disease that wreaks havoc on memory and cognition. Extracellular plaques composed of amyloid peptides and intracellular neurofibrillary tangles of hyperphosphorylated tau proteins are two neuropathological markers of Alzheimer's disease. Currently, there is no medicine that can cure, stop, or even delay the disease's progression. In this paper, a mathematical model of AD is developed that incorporates pyramidal neurons, hyperphosphorylated tau proteins, microglia, and peripheral macrophages to calculate dendrites' complexity. A set of partial differential equations represents the model by incorporating Aβ cascade, tau, and oxidative stress hypothesis. Real-time simulations have been performed to validate the different types of medications that have failed or are presently undergoing clinical trials.

#### On dark matter, dark energy and Bose-Einstein condensate

Igor Nikitin1

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

###### Abstract

Equation of state for Bose-Einstein condensate is evaluated in two cases: non-interacting particles and particles interacting via potential possessing a non-trivial minimum. In astrophysical context, the first case becomes equivalent to cold dark matter, while the second case -- to dark energy. A particular cosmological scenario with dark matter injection from quasi-black holes to galactic halo, followed by Bose-Einstein condensation in the intergalactic medium is considered.

#### Quantum superradiant entanglement of a bipartite system in Schwarzschild space-time

mohamed abdelouahab1 , Mounir BOUSSAHEL2

1University of M'sila - Mohamed Boudiaf - Algeria, physics department/ Physics and Chemistry of Materials Laboratory,, Algeria
2Université de M'Sila, Laboratoire Physique et Chimie des Matériaux, Département de Physique, Algeria

###### Abstract

In this work, our main goal was to extend quantum entanglement to superradiance. For this, it was necessary to identify the common point between the two physical concepts. This is what has been proposed and achieved, thanks to the common properties carried by the wave function solution of the Klein Gordon equation which defines the bipartite system at spin ½ in a Schwarzschild space time. A detailed study was completed where it was found that superradiance extended to quantum entanglement is more robust so far it is from the black hole.

#### Modeling the stratospheric aerosol sources optimal space distribution for climate stabilization

Valeriy Parkhomenko1

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

###### Abstract

Global warming climate changes are observed in recent decades. These changes largely associated with anthropogenic increases in greenhouse gases in the atmosphere (CO2 – most important among them). The problem and opportunity of the global climate stabilization at a current level were investigated early. The current study is based on a three-dimensional hydrodynamic global climate coupled model, including ocean model with real depths and continents configuration, sea ice evolution model and atmospheric general circulation model. Aerosol concentration from the 2010 up to 2100 year is calculated as a controlling parameter to stabilize mean year surface air temperature. It is investigated opportunity to get prescribed space and time global distribution of the stratosphere aerosol when exist limited number of aerosol sources. Wind transport and deposition of aerosol are taken into account.

#### On local solvability of the nonlinear integro-differential equation of peridynamics

Asal Yuldasheva1

1Tashkent branch of Moscow State University, applied mathematics and informatics, Uzbekistan

###### Abstract

The peridynamic theory is a nonlocal theory of continuum mechanics based on an integro-diﬀerential equation without spatial derivatives, which can be easily applied in the vicinity of cracks, where discontinuities in the displacement ﬁeld occur. This paper studies the Cauchy problem for nonlinear equation of the peridynamics. The issues of local well-posedness and smoothness of the solutions are discussed.

#### Holomorphic representation of the Calogero-Moser system

Ibrahim Nonkané1 , Frederic Y2 , Latévi Lawson3 , ALIDA ZINSOU4

1Université THOMAS SANKARA, Département d'Economie et de Mathématiques appliquées, IUFIC, Burkina Faso
2Institut des Sciences et Technologies, Ecole Normale Supérieure, Mathématiques, Burkina Faso
3African Institute for Mathematical Sciences (AIMS) Ghana, Department of Mathematics, Ghana
4Université THOMAS SANKARA, IUFIC, Burkina Faso

###### Abstract

In this note, we study the action of the Calogero-Moser system on the algebra $\mathcal{H}(\mathbb C^n)$ of holomorphic functions over the complex field $\mathbb{C}^n$. We consider the algebra $\mathcal{D}$ of invariant differential operators with analytic coefficients under the symmetric group and its representation on $\mathcal{H}(\mathbb C^n)$. We elaborate the irreducible decomposition of $\mathcal{H}(\mathbb{C}^n)$ as a module over $\mathcal{D}$. We explicitly describe the irreducible component by giving it generators.

#### Faceted-Rough Surface between Thermodynamically Rough and Atomically rough Surfaces

Noriko Akutsu1

1Osaka Electro-Communication University, Faculty of Engineering, Japan

###### Abstract

The faceted shape in a growing crystal is often observed in the materials which are necessary to sustain our daily life. The phase-field modeling of ice in a mesoscopic scale reproduces snow like the faceted dendritic shapes of a crystal [1]. Silicon (Si) crystal grown from its melted state can form faceted dendrites in a sub-millimeter scale caused by the Mullins-Sekerka instability [2]. Silicon carbide (SiC) crystal grown from Si melted state forms {\it faceted} macrosteps which degrade the quality of a crystal [3]. Theoretically, both the phase-field modeling and the Mullins-Sekerka instability assume thermodynamically rough crystal surfaces. However, in equilibrium, the faceted shape is directly connected to the thermodynamically smooth surface, where surface quantities become singular [4, 5]. Hence, the atomically rough surface has been regarded as the nano-scale rough surface, though some of the atomically rough surfaces are thermodynamically smooth in equilibrium. Here, another scenario using the faceted-rough surface [6] is proposed to explain how the atomically and thermodynamically smooth surface in equilibrium becomes a thermodynamically rough surface in a growing crystal.

[1] Demange, G; Zapolsky, H.; Patte, R.; Brunel, M. npj Comutaional Materials, (2017), 3, 15, 1--7.
[2] Tokairin, M.; Fujiwara, K.; Kutsukake, K.; Usami, N.; Nakajima, K. Phys. Rev. B, (2009), 80, 174108, 1--4.
[3] Mitani, T.; Komatsu, N.; Takahashi, T.; Kato, T.; Harada, S.; Ujihara, T.; Matsumoto, Y.; Kurashige, K.; Okumura, H. J. Cryst. Growth, (2015), 423, 45--49.
[4] Akutsu, N.; Akutsu, Y. J. Phys. Soc. Jpn., (1987), 56, 1443--1453.
[5] Akutsu, Y.; Akutsu, N.; Yamamoto, T. Phys. Rev. Lett., (1988), 61, 424--427.
[6] Akutsu, N. Sci. Rep., (2021), 11, 3711, 1-11.

###### Acknowledgements:

This work was supported by KAKENHI Grants-in-Aid (no. JP17K05503) from the Japan Society for the Promotion of Science (JSPS). This work was supported in part by the Collaborative Research Program (2020 S2-1, 2021 S3-5) of the Research Institute for Applied Mechanics, Kyushu University.

#### Variational synthesis of dynamical systems with elastic properties into element base

1ITMO University, Faculty of Control Systems and Robotics, Russian Federation
2ITMO University , , Russia

###### Abstract

We consider the synthesis problem of dynamical systems relating to a class of conditional variation problems with variable endpoints. Variational method is applied for research of the elastic oscillator with controllable spring sti ness. In solving a general conditional variation problem, the obtained di erential system of equations in closed form is studied for design of an optimal system for the initial dynamic object with a given quality functional. Transversality condition in the variational problem is formulated in terms of local programming. An optimal algorithm is constructed in the elastic oscillator, and the value of nite transition period is found.

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#### Representation of position-deformed Heisenberg algebra with maximal length

Latévi Lawson1 , Ibrahim Nonkané2

1African Institute for Mathematical Sciences (AIMS) Ghana, Department of Mathematics, Ghana
2Université Thomas Sankara, Departement d'economie et mathématiques appliquées, Burkina Faso

###### Abstract

Position-deformed Heisenberg algebra with maximal length uncertainty has recently been proven to induce strong quantum gravitational ﬁelds at the Planck scale [2022 J. Phys. A: Math. Theor. 55 105303] In the present study, we construct a Hilbert space representation in the spectral representation of this length scale. We show that the spectral representation of this length scale forms a family of discrete eigenvalues that describes a lattice space. We also construct the corresponding Fourier transform and its inverse representations. Finally, we study its deformed translation symmetry.

#### Quadratic programming for estimating the intensity of intermittent emissions from a point source of air pollution

David Parra-Guevara1 , Yuri Skiba2

1National Autonomous University of Mexico, Institute of Atmospheric Sciences and Climate Change, Mexico
2National Autonomous University of Mexico, Institute of Atmospheric Sciences and Climate Change, Mexico

###### Abstract

A method for estimating the intensity of intermittent emissions of an air pollutant from a point source is presented. The intensity parameters are obtained using time series (data) of pollutant concentrations recorded at the monitoring site. A well-posed model of atmospheric dispersion and its adjoint model are formulated for estimating the pollutant transfer from the source. Such dispersion models are used to establish relationships between the intermittent emissions from the source and data. The parameter estimation method is formulated as a quadratic programming problem which depends on the regularization parameter. The existence and uniqueness of a solution to this optimization problem are proved. Particular solutions of the dispersion model are used to establish the constraints of the quadratic programming problem. We stress out the computing advantage of using adjoint functions to compute such solutions. One-dimensional synthetic numerical examples demonstrate the capability of the method for estimating the intensity of intermittent emissions.

###### Acknowledgements:

This research was supported by the grants 25170 and 14539 of the National System of Investigators (SNI-CONACyT, México).

#### Lewis-Riesenfeld quantization of damped harmonic oscillator

Latévi Lawson1 , Ibrahim Nonkané2

1African Institute for Mathematical Sciences (AIMS) Ghana, Department of Mathematics, Ghana
2Université Thomas Sankara, Departement d'economie et mathématiques appliquées, Burkina Faso

###### Abstract

The damped harmonic oscillator is one of the fascinating systems that have remained over years a constant source of inspiration in quantum physics. It has attracted much attention in the literature since the problem related to this system is far from having a satisfactory solution. In fact, the quantization of dissipative systems well known in the literature as Caldirola and Kanai system has been criticized for violating certain laws of quantum theory such as the zero-point of the expectation values of the energy instead of going to the quantum ground energy and the violation of the Heisenberg uncertainty relations when one tends the time to inﬁnity. In this paper, we provide a complete solution to this problem using the Lewis-Riesenfeld procedure of invariant

#### The damped harmonic oscillator in the deformed Poisson brackets

Latévi Lawson1 , Ibrahim Nonkané2

1African Institute for Mathematical Sciences (AIMS) Ghana, Department of Mathematics, Ghana
2Université Thomas Sankara, Departement d'economie et mathématiques appliquées, Burkina Faso

###### Abstract

Valtancoli in [J. Math. Phys. 56, 199 (2015)] has shown how the deformation of the canonical transformations can be made compatible with the deformed Poisson brackets. Based on this work, through an appropriate canonical transformation, we solve the problem of a one-dimensional damped harmonic oscillator in the framework of the deformed Poisson bracket. We show that the equations of the motion can be described by trigonometric functions with frequency and period depending on the deformed and the damped parameters. We eventually discuss the inﬂuences of these parameters on the motion of the system.

#### Design of multiplier less compensator for multistage decimation filter

Gordana Jovanovic Dolecek1

1Institute national INAOE Puebla Mexico, Electronics, Mexico

###### Abstract

This paper presents the design of the compensator for a multistage decimator recently proposed in the literature. The multistage decimator requires a minimum number of adders per output sample (APOS) for a given minimum folding band attenuation. We design the compensator for a a narrowband and wideband cases. The magnitude characteristic of the compensator is given as a product of two sinusoidal functions and the amplitude of the sinusoidal functions are parameters of design. We propose to use particle swarm optimization to find the parameters of design. To obtain a multiplier less design the obtained design parameters are presented in a power-of-two form. The results of narrowband and wideband designs are illustrated with examples.

#### Faraday waves in alternating multi-layer systems in microgravity

Isabel Torres Parra1 , Pablo Salgado Sánchez2 , Jeff Porter3

1Escuela Técnica Superior de Ingeniería Aeronáutica y del Espacio, E-USOC, Center for Computational Simulation, Spain
2Escuela Técnica Superior de Ingeniería Aeronáutica y del Espacio, , Spain
3Escuela Técnica Superior de Ingeniería Aeronáutica y del Espacio, , Spain

###### Abstract

Motivated by recent experiments [Salgado Sanchez et al. J. Fluid Mech. 865, 850-883 (2019)] and theory [Labrador et al. J. Phys.: Conf. Ser. 2090, 012088 (2021)], we present a theoretical investigation of Faraday waves in alternating multi-layer systems in microgravity. A linear stability analysis is used to study the system dynamics near the primary subharmonic instability, extending the results of Labrador et al. (2021) to a finite number of layers $\mathcal{N}$. For an odd number of layers $\mathcal{N} = 2 N + 1, \: N \in \mathbb{N}^+/\{ 0 \}$ (thus, an even number of interfaces $\mathcal{N} - 1 = 2 N$), Faraday waves appear via multiple Hopf bifurcation, with $N$ distinct frequencies. For an even number of layers $\mathcal{N} = 2 N, \: N > 1$ (thus, an odd number of interfaces), the set of primary Hopf bifurcations is accompanied by a pitchfork bifurcation within a subspace where the multi-layer problem is equivalent to $N$ isolated systems of two layers; the unstable dynamics in this subspace is analogous to that of a single oscillator. These theoretical results are complemented by numerical simulations for the relatively simple cases of $\mathcal{N} = 3,\, 4$ and $5$ alternating layers of the immiscible liquids FC-40 and 20~cSt silicone oil. Simulations are consistent with a primary Hopf bifurcation that can be either subcritical or supercritical depending on the applied forcing frequency (detuning). In the subcritical regime, this primary bifurcation is accompanied by a saddle-node bifurcation that stabilizes the branch of unstable solutions created at onset. After this turning point, the stable modulated solutions are destroyed in a saddle-node heteroclinc bifurcation.

#### Stochastic Model for mRNA Translation with Applications to Yeast

Madeline Brazil1 , Kyle Friend2 , Frederick LaRiviere3 , Dan Mazilu4 , Irina Mazilu5 , Laurentiu Stoleriu6

1Washington and Lee University, Physics and Engineering, United States
2Washington and Lee University, Chemistry and Biochemistry, United States
3Washington and Lee University, Chemistry and Biochemistry, United States
4Washington and Lee University, Physics and Engineering, United States
5Washington and Lee University, Physics and Engineering, United States
6Al. I. Cuza University, Physics, Romania

###### Abstract

We present a generalized totally asymmetric exclusion process (TASEP) model inspired by the complex process of mRNA translation. The main goal of the project is to build the analytical and computational framework in order to be able to solve numerically a variety of master equations associated with different applications and variations of this general model. In the context of the mRNA translation, the mRNA strand is represented by a one-dimensional lattice with its sites playing the role of the codons. The ribosomes are moving along the lattice with translation rates that are site dependent. We derive and solve the associated master equation using numerical methods. We present results on the time evolution of the particle density and particle currents. In particular, we discuss a yeast-specific model customized for two different cases: an infinite ribosome pool model and a more realistic finite ribosome pool model. For each of the cases we also introduce ribosome size exclusion where the volume occupied by a single ribosome is taken into account. This model is versatile and can be modified to represent mRNA translation for other types of cells or traffic-like physical systems.

#### On the Accuracy of Calculating Unstable Normal Modes of a Viscous Flow on a Sphere

Yuri Skiba1

1National Autonomous University of Mexico, Institute of Atmospheric Sciences and Climate Change, Mexico

###### Abstract

The work deals with the method of normal modes used for the linear stability study of solutions to the barotropic vorticity equation for a viscous and forced fluid on a rotating sphere. It is the most effective and constructive technique allowing to find exponentially growing perturbations at the initial stage of the instability when the perturbation is still small and their behavior is well described by the linearized equation. Instead of the classical Navier-Stokes form (s=2), a real degree s of the spherical Laplace operator (s≥2) is considered in the viscosity term. Hyperdiffusion of this sort is used because ordinary linear diffusion is often too dissipative for many applications. In the framework of the normal mode method, the original nonlinear equation is linearized with respect to infinitesimal perturbations of the basic solution, and the perturbations are sought in the form of normal modes as the product of a function of time and a function of spatial variables. The function of time determines the exponential growth or decay of the mode, while the function of spatial variables represents the mode amplitude. The search for unstable perturbations reduces to the solution of the eigenvalue problem for the linearized operator. It is proved that the operator linearized about the basic flow has a compact resolvent. The spectral theory for compact operators by Bramble and Osborn (1973) is used to estimate the accuracy of calculating the unstable normal modes. The estimates show that the accuracy of the spectral approximation improves as the smoothness of the functions and the degree s in the viscosity term of the barotropic vorticity equation increase.

###### Acknowledgements:

The author thanks the National System of Researchers (SNI, CONACYT, Mexico) for scholarship 14539.

#### Numerical computation of the Lyapunov exponents for the soft stadium family

Julio S. Espinoza-Ortiz1

1Federal University of Catalão, Physics, Brazil

###### Abstract

It is well known that the characteristic Lyapunov exponents values represent a quantitative measure concerning stochastic properties of a dynamical system, arising from the exponential divergence of neighboring orbits computed as time evolves. We apply this basic concept to compute the largest Lyapunov exponent for the soft quarter-stadium, a smoothed system via an exponent monomial potential. This realistic system is partially reflective preserving the particle’s translation and rotational motion into the respective regions of a well defined Bunimovich like quarter-stadium. It is integrable for the exponent value equal to one and so by increasing it, the system's boundaries begin to be even more rigid and its dynamics reaches a complete chaotic regime. We compute the largest Lypaunov exponents for significant values of the monomial exponent potential, and also compare these orbits' divergences measured for the soft stadium's family with the billiard case.

#### First Principles Study of Bi2Fe4O9 in the Hybrid HSE06 Approach

Deimer Gómez-Mejía1 , Omar Jiménez-Sandoval2 , Daniel Olguín3

1Centro de Investigación y de Estudios Avanzados del IPN, Unidad Querétaro, Mexico
2Centro de Investigación y de Estudios Avanzados del IPN, Unidad Querétaro, Mexico
3Centro de Investigación y de Estudios Avanzados del IPN, Departamento de Física, Mexico

###### Abstract

Mullite-type ternary oxides Bi2M4O9 (M = Fe3+, Al3+, Ga3+) are interesting materials intended for use in multiple applications such as gas sensors, electrochemical reactors, fuel cells, photocatalysis, photoelectrochemical water splitting, among others. It is widely accepted that knowledge of the electronic properties of these systems allows the evaluation of their potential applications. In order to contribute to the study of these systems, we present in this work first principles calculations of ferromagnetic metal oxide Bi2Fe4O9. In our calculations we have used the Quantum Espresso code with norm conserving pseudopotentials, while for the exchange-correlation energy we have used the hybrid HSE06 approach. As we have found, the material shows semiconductor properties with a calculated band gap value of 2.0 eV. From the calculated density of states, it is observed that the main contribution to the energies at the Fermi level comes from the hybridization of the Fe “d” states with the O “p” states, whereas the contribution of the Bi states is obtained in the lower valence bands as well in the conduction bands. Our results are in good agreement with experimental data, as well as with reported DFT+U calculations.

###### Acknowledgements:

The authors are grateful to Héctor M. Oliver-Hernández for technical assistance in some calculations, and for the computing time granted by LANCAD in the Supercomputer Hybrid Cluster Xiuhcoatl at GENERAL COORDINATION OF INFORMATION AND COMMUNICATION TECHNOLOGIES (CGSTIC) of CINVESTAV (URL: http://clusterhibrido.cinvestav.mx/). We are also grateful to the National Council for Science and Technology (Conacyt, México) for financial support through Grant No. A1-S-28734.

#### Collocation Method with GeoGebra in linear second order differential equation

Jorge Olivares1 , Maria Drina Rojas2 , Pablo Martín de Julián3

3Universidad de Antofagasta, physics , Chile

###### Abstract

In this article, we will show how to find approximate solutions, using the numerical analysis Collocation method with the GeoGebra software to the second order linear differential equations of the form d^2y/dx^2+A(x)dy/dx+B (x)y=Q (x), y (0) = y (a) = 0, where "a" is a positive number. The use of GeoGebra in the numerical analysis allows us to simultaneously, interactively and dynamically view the solutions and approximations of the differential equations.

#### A Monte Carlo approach for the fully probabilistic evaluation of operability in Ship Dynamic Positioning scenarios.

1NASDIS PDS d.o.o., HYDRODYNAMIC DEPARTMENT, Slovenia
2University of Strathclyde, Department of Naval Architecture, United Kingdom

###### Abstract

The Dynamic Positioning system allows a vessel to keep a precise position and heading during stationing operations in a rough sea by using onboard actuators only. During the design phase, it is mandatory to identify the capability of the system actuators to counteract the environmental forces. Conventional predictions are limited to the estimation of a maximum sustainable wind speed on predefined encounter angles by estimating the corresponding wave parameters with questionable standard deterministic correlations. The proposed approach aims at determining the dynamic positioning performances by using site-specific long-term environmental conditions which are modelled with joint distributions of wind and wave parameters. To this end, the operability of the dynamic positioning system is evaluated as a non-deterministic multidimensional Monte Carlo integration process, based on the sampling of environmental joint distributions. For each environmental condition, a quasi-static dynamic positioning analysis is performed solving the equilibrium between external forces and the vessel’s actuators through a non-linear thrust allocation algorithm. The proposed methodology is applied to a reference offshore ship in two different operative geographic areas, highlighting the suitability of the calculation methodology for site-specific operability predictions.

#### Stationary analysis for coupled nonlinear Klein-Gordon equations with asymmetric parameter settings

Yoritak Iwata1

1Kansai University, Faculty of Chemistry, Materials and Bioengineering, Japan

###### Abstract

Klein-Gordon equations describe the dynamics of waves/particles in sub-atomic scales. For a system of nonlinear Klein-Gordon equations, systematic analysis has been carried out for those stationary problems [1]. In the present study, the parameters (mass, wave propagation speed, and the force parameters) are chosen to be asymmetric between the two single equations, although the parameters are taken to be symmetric in our previous research [1]. Asymmetric parameter settings are equivalent to assume the interacting two different particles. In this paper, based on the high-precision numerical scheme [2], the appearance and existence of nonlinear oscillatory mode is studied for a coupled nonlinear Klein-Gordon equations with spatial boundary condition. The competition, coherence, and decoherence of different waves are shown to appear depending on the choice of asymmetrically-implemented parameter values. In conclusion, the conditional existence of nonlinear oscillatory mode is presented, and its compact manifolds inside the infinite-dimensional dynamical system is shown. [1] Yasuhiro Takei, Yoritaka Iwata, Stationary analysis for coupled nonlinear Klein-Gordon equations submitted; arXiv:2109.11038 (presented at C-MSQUARE 2021). [2] Yasuhiro Takei, Yoritaka Iwata, Numericnal scheme based on the implicit Runge-Kutta method and spectral method for calculating onlinear hyperbolic evolution equations, Axioms 2022, 11 (1) 28.

#### A Group Theory Approach in the Analysis of Temperature Symmetry in Semiconducting Junction Devices

Richard Ocaya1

1University of the Free State, Physics, South Africa

###### Abstract

The temperature behavior remains one of the most important fundamental properties of any given system linked inextricably to the other parameters of the system. However, despite this importance, it remains the least framed and explored properties of most systems for many reasons. The effects of temperature constrain most analyses to a constant or narrow domain where its impact on the other parameters is minimal. Even in systems where an analytical form may be available, the parametric expression of the system may possess an overall complexity that necessitates a reduced functional domain, thereby limiting the usable range. Nowhere is this more apparent than in the case of semiconducting junction devices with energy barriers that are complex functions of temperature, current density, and bias. In previous work, we showed that, at a given temperature, the current-voltage characteristics have translational symmetry despite the apparent complexity of the expression. In this work, we extend the use of group theory in the non-linear analysis of temperature symmetry by examining the case of a simple p-n junction device. The results prove the existence of a temperature symmetry and thus provide a new direction for the wide-domain analysis of temperature effects in a given system.

#### Numerical bifurcation analysis of the steady ABC flow: preliminary results

Nikolay Evstigneev1

1Federal Research Center ''Computer Science and Control'' of the Russian Academy of Sciences, Macrodynamic systems, Russian Federation

###### Abstract

The classical Gromeka--Arnold--Beltrami--Childress (ABC) flow for the stationary 3D Navier-Stokes equations on a torus for velocity vector function $\mathbf{u}:\mathbb{T}^3 \to \mathbb{R}^3$ and pressure scalar function $p:\mathbb{T}^3 \to \mathbb{R}$ is considered as: $$(\mathbf{u}, \nabla) \mathbf{u} + \nabla p - \frac{1}{R}\bigtriangleup \mathbf{u} - (\sin(z)+\cos(y); \sin(x) + \cos(z); \sin(y) + \cos(x))^\mathrm{T} = 0,$$ $$\nabla \cdot \mathbf{u} = 0,$$ where $R$ is the Reynolds number (bifurcation parameter), the torus domain $\mathbb{T}^3:=[0;2\pi] \times [0;2\pi] \times [0;2\pi]$ and $\bigtriangleup$ is the Laplace operator. A finite dimensional system of equations can be obtained in the Fourier space (designated as $\hat{\mathbf{u}}$) using the Galerkin method that can be written as: $$F(\mathbb{P}\mathbf{\hat{u}}) = 0,$$ where the pressure is eliminated from the system by the projection operator $\mathbb{P}:=(id - \nabla \bigtriangleup^{-1} \nabla \cdot)$ and the forcing term is consumed into the nonlinear operator $F$. This paper is focusing on the numerical investigation of the finite dimensional Fourier-Galerkin system (using $(256) \times (256)\times(256)$ Fourier harmonics), construction of the solution curves in the parameter-phase space and analysis of disconnected solutions. The paper presents bifurcation diagrams.

#### “The simulation of gravitational acceleration using a model of the compressible viscous Navier Stokes differential equations”

rensley meulens1

1Elux Technologies B.V., Research & Development, Netherlands Antilles

###### Abstract

Out of the analytical results of the innovative paper" A note on N-soliton solutions for the viscid incompressible Navier– Stokes differential equation", AIP Advances 12, 015308 (2022), https://doi.org/10.1063/5.0074083 by r. meulens becomes it clear that the solutions for the (in)compressible Navier Stokes differential equations are locally curved. Since the N-soliton based vorticity and velocity tensors solutions are directly and tangentially related to the space-like and time-like variables of non-linear wave-phenomenons, implicates that the last variables are also curved in the benchmark analyzed problems. Using the buoyancy model principles of Archimedes and the compressible and viscid Navier Stokes d.e. it became clear that the (artificial) gravity is velocity dependent and therefor quantized and can be calculated out of the solutions presented in the referenced paper. The velocity is a solution of the Eigenvalue problem of a quantum harmonic oscillator. This article gives the necessary building stones to introduce the omne mechanicae for the unification of the four forces in nature in one set of momentum, continuity eqs. (as modeled by the Navier Stokes d.e.) complemented with situational state equations depended on the thermodynamical conditions of the sample volume. This article also addresses and does explain some other unsolved paradigms of physics like the information paradox and the problems with the cosmological constant which are automatically solved with the introduction of the Navier Stokes d.e.to model cosmological processes.

#### "Exact distributions for the solutions of the compressible viscous Navier Stokes differential equations: an application in the aeronautical industry"

rensley meulens1

1Elux Technologies B.V., Research & Development, Netherlands Antilles

###### Abstract

Wind tunnels and linearized turbulence and boundary-layer models have been so far necessary to simulate and approximate the stationery lift and drag forces on (base-mounted) airfoils by means of statistically determined or approximated values of the relevant situational coefficients as the drag and lift coefficients. To improve this process, we introduce transient and exact formulae to separate these forces in advance by means of the solutions found from the fluid dynamics model of the Navier Stokes differential equations.

#### Chaos and hyperchaos in nonlinear systems of differential equations

Nikolai Magnitskii1

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

###### Abstract

In modern literature on nonlinear and chaotic dynamics, it is believed that hyperchaos in nonlinear systems of ordinary differential equations is characterized by the presence of at least four equations and at least two positive Lyapunov exponents [1-3]. The paper shows that the leading characteristic exponent is equal to zero for any singular attractor, and transition to hyperchaos in nonlinear systems of differential equations occurs, as in any other nonlinear chaotic systems, in accordance with the Feigenbaum-Sharkovsky-Magnitskii (FShM) universal bifurcation scenario [4-6]. In case of hyperchaos, in contrast of chaos, the infinitely sheeted surface of the two-dimensional heteroclinic separatrix manifold (separatrix zigzag), which contains both all singular attractors and all cycles of the system, born as a result of all infinite cascades of bifurcations, is split due to the presence of an additional fourth dimension. 1. Li Y., Wei Z. and Aly A. A 4D hyperchaotic Lorenz-type system. Eur. Phys. J. (2022), 00448-2. 2. Yang J., Wei Z. and Moroz I. Periodic solutions for a four-dimensional hyperchaotic system. Advances in Difference Equations. (2020), 2020:198. 3. Djondiné1 P., Malobé P. A. Generation of hyperchaos from the Lü system with a sinusoidal perturbation. J. App. Math. and Phys. 9 (2021), P.1100-1107. 4. Magnitskii N.A. On the topological structure of singular attractors of nonlinear systems of differential equations. Differential Equations. 46, 11 (2010), P. 1552–1560. 5. Magnitskii N.A. Universality of Transition to Chaos in All Kinds of Nonlinear Differential Equations. Chapter in Nonlinearity, Bifurcation and Chaos - Theory and Applications. Rijeca: InTech. (2012). P. 133-174. 6. Magnitskii N.A. Bifurcation Theory of Dynamical Chaos. Chapter in Chaos Theory. Rijeka: InTech. (2018), P.197-215

#### Modeling Electrochemistry

Sara Vesely1

1ITB-CNR (retired), ITB-CNR (retired), Italy

###### Abstract

The sciences of matter include a number of disciplines closely concerning the world around us and look like a patchwork. Since our world is subject to continuous change, virtually every new undertaking or insight invites to a revised approach, beginning with the simplest chemical reactions in homogeneous solutions. Understanding how chemical changes occur is demanding. Currently, to deal with selective chemical conversions taking intermediates and branched reactions into account, mathematical models resort to stochastic processes. Given that there are always several modeling choices, the main mathematical problem lies in meaningfully linearizing the equations ruling the reactions. In addition, in case one wishes to pursue a new approach, as is sustainable development, perhaps the handed down equations are doomed to become opaque. For an example, let’s just focus on yield increase, dispensing with labeling the developments in the making as for their social, economic, and environmental impact. Stimulated selective changes, to wit, resonance conditions, can lend themselves to outperformance with respect to changes occurring in a near-linear range. There may be some doubt whether driving selective processes to obtain high yields is a sustainable development. That notwithstanding, let’s ask how to model the relevant changes. In all likelihood, dealing with the problem of increasing reaction or power yield beyond the linear regime lies outside thermodynamics, at least inasmuch as it becomes a nonlinear problem, that can only be solved in a small region around a given operating point. Moreover, we expect a significant increase of the yield of a process above the value established by the energy conservation principle to break thermodynamics. Predictive models using probability theory, too, cease to be valid beyond the linear range, so that mechanical statistical methods aren’t so good. Finally, computational modeling of selective and specific processes by a systematic refinement that includes each property of the phenomenon is prohibitively complicated. As an alternative, signal reception techniques could be employed to monitor the signals associated to those processes. While the latter are highly nonlinear, if a linear signal response can be adjusted to fit the produced change in yield, the process at stake can be followed experimentally, and modeled, by suitably parametrizing the linear response. Mathematical models of the signal changes can assist more general insights, and heuristic guesses. Faraday’s investigations on electrolysis can be viewed as a first failed effort in this direction. On the one hand, in Faraday’s time circuit design was not as advanced as today, and on the other, his approach lends itself to open a more general avenue in the understanding of selective and specific processes. We try and put electrolysis in context.

#### Applications of Travel Time Principle to Measure River Flow Dynamics in a Shallow Mountain River

###### Abstract

Accurate and advanced measurement of river flow in remote areas such as mountainous streams is important for developing and improving the current physical and hydrological models. The objective of this study is to utilize the fluvial acoustics tomography (FAT) system as an advanced tomographic instrument to evaluate river temperature, velocity, and discharge based on the travel time principle. First, a pair of the FAT system were placed on both riverbanks, then reciprocal sound transmission between the acoustic stations was performed and measured to compute the sound speed and hence both stream velocity, and streamflow. In addition, stream temperature was computed using sound speed. To verify the accuracy of our measurement, comparisons with other records were performed. Overall, this paper presents an advanced and promising system capable to provide reliable records of river flow characteristics.

###### Acknowledgements:

This study was supported by JSPS KAKENHI grant number JP21K14253.

#### Formation of Stable Standard Movements of a Loaded Platform of a Dynamic Simulation Stand

Victoria Petrova1

1Saint Petersburg State University, Mathematics and Mechanics Department, Russian Federation

###### Abstract

Dynamic simulation stands are widely used for training aircraft pilots and drivers of various vehicles. An integral part of such stands is the Stewart platform, driven by six rods of variable length (for example, hydraulic cylinders). The report confirms a well-known fact about the instability of the movements of the stand platform. Even the equilibrium position of the platform turns out to be unstable, in particular, due to the presence of "parasitic" fluctuations. To implement a steady movement, it is necessary to introduce feedbacks. The report examines the formation of stable standard movements of the loaded platform of the stand. Vertical and lateral movements of the platform and its rotations are considered when changing the angles of yaw, pitch and roll. The results of some calculations of the movement of the Stewart platform loaded with the cabin of some hypothetical heavy truck are presented.

#### Exploratory Research and Practical Application on Life-cycle Carbon Emission Calculation Method for Near-zero Carbon Buildings

Yazhou Ou1 , Yuqi Xiao2 , Jin Wang3 , Jiantao Li4

1China Construction Eighth Engineering Division Co., Ltd, Engineering research Institute, China
2China Construction Eighth Engineering Division Co., Ltd, , China
3Saint-gobain research (Shanghai) co., ltd., , China
4China Construction Eighth Engineering Division Co., Ltd, , China

###### Abstract

This paper mainly presents a calculation method of carbon emission (in CO2 equivalent) in the whole life cycle of buildings and its application in a construction project. The energy consumption calculation formula is established according to items in each sub-projects, and the carbon emission factors are selected based on experiments, experience reference and relevant standards. The CO2 emission of each sub-project in the current stage can be obtained by summation of items. Reference data are from NREL-USLCI Database (U.S. LCI) and Chinese Reference Life Cycle Database (CLCD). Via comparing the carbon emission factors of the same material in different databases, a linear relationship is regressed, so that the data could be optimized and supplemented. Data were collected during the building process, and the overall carbon emission equivalent values of buildings at different stages of design, material production, processing, transportation, construction, demolition, operation and maintenance were statistically calculated, including materials, equipment and plants with carbon sink effect should be taken into consideration. Through a series of measures, including optimization of architectural design, adoption of low-carbon production and construction technology, reduction of energy consumption, and increase of renewable energy and carbon sink usage, the carbon emission of the building will be significantly reduced to near zero. It can provide guidance and other helpful information for the development of low-carbon and eco-friendly construction in the future.

#### Weak values in strong measurements

Francisco De Zela1

1Pontificia Universidad Católica del Perú, Physics, Peru

###### Abstract

In 1988, Aharonov, Albert and Vaidman (AAV) introduced the concept of quantum weak values (WVs). This rather counterintuitive feature of quantum mechanics eventually evolved into a tool that is widely used for various purposes, including both theoretical approaches and practical applications. The theoretical basis of WVs was von Neumann's model of quantum measurements. In this model, a system is submitted to measurement by coupling it to a ''pointer''. One deals with two observables; one of them, $\hat{A}$, is related to the system and the other, $\hat{P}$, is related to the pointer. System and pointer evolve under the action of the coupling Hamiltonian $\hat{H}=g \hat{A}\otimes \hat{P}$. Measuring $\hat{X}$, the conjugate operator to $\hat{P}$, i.e., $[\hat{X},\hat{P}]=i$ , means to read out the pointer's position. From the pointer's reading, one derives the value of the system's observable. When the system-pointer coupling is weak, one may perform a low-order Taylor expansion for the evolution operator $\hat{U}$ of system and pointer. This was assumed by AAV and constitutes the standard approach to WVs. The latter are defined as the complex number $$A_w=\frac{\langle f|\hat{A}|i\rangle}{\langle f|i\rangle},$$ where $|i\rangle$ and $|f\rangle$ are two system states that can be conveniently chosen. AAV showed that $A_w$ could take on values outside the range of $\hat{A}$'s eigenvalues, something that was seen as an odd feature, giving rise to much debate. AAV's approach ties WVs to weak couplings. WVs appear at the lowest-order Taylor expansion of the unitary operator $\hat{U}(\epsilon)=\exp(-i \epsilon \hat{A}\otimes \hat{P})=\hat{I}-i\epsilon \hat{A}+\ldots$, where $\epsilon=g \tau \ll 1$ and $\tau$ is a pulse-like interaction time. We have explored the strong-coupling case and obtained closed-form expressions containing WVs. We report such expressions in this work. Our results open the way for extending the applicability of WVs to the strong-coupling regime and their associated strong measurements. We discuss one of these cases and show how WVs may appear when dealing with both single photons and classical light beams. This illustrates that WVs are not a purely quantum feature, but a feature that stems from the underlying, linear vector-space structure of quantum and classical models.

###### Acknowledgements:

US Office of Naval Research Global (ONR, Award No. N62909-19-1-2148, Grant No. GRANT12853637)

#### Violation of the Einstein’s Equivalence Principle for a Composite Quantum Body

Andrei Lebed1

1University of Arizona, Department of Physics, United States

###### Abstract

Recently, we have started to investigate behavior of a composite quantum body in an external gravitational field in the framework of General Relativity [see, for a review, A. G. Lebed, Mod. Phys. Lett. A, vol. 35, 2030010 (2020)]. As the simplest example, we have considered a hydrogen atom in a weak gravitational field. Our results are the following. The Einstein's Equivalence Principle survives for the most of macroscopic ensembles of the atoms, containing the stationary quantum states. On the other hand, we have demonstrated that this principle is sometimes broken. In particular, it is broken for the so-called Gravitational demons, which are the coherent macroscopic ensembles of two or more stationary quantum states in the hydrogen atoms. In the above cited paper we have considered the Gedanken experiment, where the gravitational field is suddenly switched on in a free from gravitation space. In the current presentation we consider much more realistic from experimental point of view Gedanken experiment and come to the same conclusion about violations of the Einstein's Equivalence Principle for the Gravitational demons.

###### Acknowledgements:

We are thankful to Natalia N. Bagmet (Lebed), Steven Carlip, Fulvio Melia, Pierre Meystre, Keneth Nordtvedt, Douglas Singleton, and Vladimir E. Zakharov for useful discussions.

#### Brain activity vs. seismicity: Scaling and memory

Sumiyoshi Abe1 , Norikazu Suzuki2

1Huaqiao University, Department of Physics, College of Information Science and Engineering, China
2Nihon University, College of Science and Technology, Japan

###### Abstract

The brain activity and seismicity share a remarkable similarity. The Gutenberg-Richter law describing a power-law relation between the frequency of earthquake occurrence and released energy has its counterpart in the brain activity of a patient with epilepsy, that is, the distribution of fluctuations of the voltage difference measured by electroencephalogram (EEG) also obeys a Gutenberg-Richter-like power law. The similarity in the distributions, however, does not directly tell if the processes underlying these intermittent phenomena are also similar to each other. Here, a simple method is presented for quantitative evaluation of (non-)Markovianity and is applied to the processes of released energy in seismicity and fluctuation of the voltage difference in EEG data. It is shown that the process in seismicity is almost memoryless, whereas that in EEG has long-term memory.

#### Existence of groud-state solution for the Schr\¨odinger-Newton equation with Aharonov-Bohm(AB) magnetic field

Frederic Y1

1Institut des Sciences et Technologies, Ecole Normale Supérieure, Mathématiques, Burkina Faso

###### Abstract

We study in this notes the dynamic of boson particles in the presence of Aharonov-Bohm(AB) magnetic field. To do so, after we model the dynamic of boson particles in the AB-magnetic field to obtain a Schr\¨odinger-Newton equation, we use technics due to Lieb based on the symmetric decreasing rearrangement inequalities to prove existence of ground-state solution.

#### SIMULATION AND CALCULATION OF THE EFFECT UNDERCUTTING OF TONEHOLES ON THE EIGENFREQUENCIES DISPLACEMENT OF WOODWIND INSTRUMENTS

Roman Gerasimov1

1Military University of Radioelectronics, Department of Physics, Russian Federation

###### Abstract

The influence of the existence and value of the radius of curvature (undercutting) at the junctions of the toneholes of woodwind instruments with the main bore on the eigenfrequencies displacement is considered. The technique and formulas for numerical calculation are presented, which allow calculating matching volume equivalent length of the tonehole depending on the degree of joint curvature, as well as the values of the effective radius of the tonehole. A numerical calculation of the eigenfrequencies of an air bore with a single tonehole was carried out and compared with the results of computer simulation in the COMSOL Multiphysics 5.5 program. It is shown that an increase of the degree of undercutting leads to an increase in equivalent length and effective radius of tonehole. This increases the resonant frequencies in the case of an open tonehole and decreases in the case of a closed tonehole.

#### Origin of anisotropic diffusion in Turing Patterns

Hiroshi Koibuchi1 , Fumitake Kato2 , Gildas Diguet3 , Tetsuya Uchimoto4

1National Institute of Technology, Ibaraki College, Industrial Engineering, Japan
2National Institute of Technology, Ibaraki College, , Japan
3 Advanced Institute for Materials Research (AIMR), Tohoku University, , Japan
4Institute of Fluid Science (IFS), Tohoku University, , Japan

###### Abstract

Turing patterns described by partial differential equations, composed of diffusion and reaction terms, are numerically studied on two-dimensional fixed-connectivity and dynamically-triangulated-fluid lattices. This equation has a time-dependent plane wave solution close to a constant solution, and the time-dependent solution possesses an unstable behavior called Turing instability. Isotropic Turing patterns can be checked numerically with suitable pairs of diffusion constants. Moreover, if the diffusion constants are direction-dependent, anisotropic patterns appear. However, the origin of this anisotropy in diffusion coefficients is unclear. We study this problem using the Finsler geometry (FG) modeling technique, which connects diffusion anisotropy with anisotropy in differentials of Laplacian. To implement such anisotropy in Laplacian, we need to include internal degrees of freedom (IDF) for distance-anisotropy on the triangulated lattices. The problem is to find the content or identity of IDF. One possible origin of this IDF is thermal fluctuations of lattice vertices. The movement of vertices is characterized by velocity, which is direction-dependent and plays a role in IDF. The velocity can be aligned to a direction specified by some external stimuli or forces. This velocity alignment, representing an actual anisotropic diffusion of lattice vertices, causes anisotropic Turing patterns on both fixed-connectivity and fluid surfaces.

#### Geometric confinement effect and stabilization of skyrmions

Hiroshi Koibuchi1 , Fumitake Kato2 , Sahbi El Hog3 , Gildas Diguet4 , Benjamin Ducharne5 , Tetsuya Uchimoto6 , Hung T. Diep7

1National Institute of Technology, Ibaraki College, Industrial Engineering, Japan
2National Institute of Technology, Ibaraki College, , Japan
3LMCN, University of Monastir, , Tunisia
4 Advanced Institute for Materials Research (AIMR), Tohoku University, , Japan
5INSA Lyon, , France
6Institute of Fluid Science (IFS), Tohoku University, , Japan
7CY Cergy Paris University, , France

###### Abstract

Skyrmions are topologically stable spin configurations in chiral magnetic materials, and their stability is one of the main topics that should be studied in view of future technological applications. An external magnetic field is a well-known ingredient for the stabilization of skyrmions, and mechanical stresses are also known to enhance the stability [1,2]. Recent experiments report that a small nano-domain confines and stabilizes skyrmions inside it [3]. This stabilization is called geometric confinement and is considered to come from the so-called surface effects, which increase with reducing size. However, the origin of this effect is unclear in the case of skyrmion. From Monte Carlo simulation data, we find that zero Dzyaloshinskii-Moriya interaction (DMI) energy on surfaces parallel to the magnetic field stabilizes skyrmions for a small magnetic field regime. This stabilization indicates that an inhomogeneous distribution of DMI energy on the bulk and surface of the material plays an essential role in the surface effect of geometric confinement. \\ [1] S. El Hog, F. Kato, H. Koibuchi and H. T. Diep, Phys. Rev. B104, 024402(1-17) (2021), https://journals.aps.org/prb/abstract/10.1103/PhysRevB.104.024402 \\ [2] S. El Hog, F. Kato F, S. Hongo, H. Koibuchi, G. Diguet, T. Uchimoto, and H.T. Diep, Results in Physics 38, 105578 (2022) https://doi.org/10.1016/j.rinp.2022.105578 \\ [3] Y.Wang et al. Nature Comm. 11, 3577 (2020), https://doi.org/10.1038/s41467-020-17354-7

#### Optical pulses in fiber medium dominated by an integrable (2+1)-dimensional nonlinear Schr\"{o}dinger system

Khalil Al-Ghafri1

1University of Technology and Applied Sciences, College of Applied Sciences, Oman

###### Abstract

The present study focuses essentially on investigating miscellaneous optical pulse structures for an integrable system of coupled (2+1)-dimensional nonlinear Schr$\"{o}$dinger equations (2D-NLSS). By means of traveling wave transformation, the model of the 2D-NLSS is simplified to an ordinary differential equation (ODE). The resulting ODE is dealt with two methods to extract the solutions of the system. The obtained solutions describe different physical structures of optical solitons such as W-shaped, bright and singular solitons. Further to this, rational function and periodic function solutions are also derived as a byproduct of solution techniques. The evolutions of retrieved optical waves are exhibited by drawing their graphs to provide clear view of the physical features of the model. The outcomes obtained can be exploited in improving the applications relevant to the field of nonlinear optics.

#### Electrode With Spatially Combined Heating Zones For Oncology Therapy

Valeriy Makarov1 , Nikita Boos2

1MIREA - Russian Technological University, Department of Bio-Cybernetic Systems and Technologies, Russian Federation
2MIREA - Russian Technological University, Department of Bio-Cybernetic Systems and Technologies, Russia

###### Abstract

The main problem of existing installations of microwave and radiofrequency thermal destruction is the insufficient amount of tissue coagulation. A design of a coaxial electrode (CE) for combined microwave (MW) and radiofrequency (RF) heating is proposed. The CE had inner and outer hollow conductors separated by a PTFE insulator and having a short circuit at the end of the CE. An annular slot is cut on the outer conductor at a distance λ/4 from the end of the CE, where λ is the wavelength of microwave radiation in the coaxial line. The outer electrode has a protective coating, part of which is missing symmetrically below and above the center of the slot on a total length of 5 to 20 mm, and the annular slot has a width of 4.0 mm. The resulting RF and microwave electrodes are connected to the RF and MW generators through a switch that allows alternate or shared use of the heating zones of the electrode. To test the approach, computer simulation of the CE was carried out in the COMSOL Multiphysics software environment, which showed the possibility of creating a heating region with a diameter larger than in the case of separate heating. The most appropriate configuration of such an electrode was selected empirically. The result of the work is the creation of a new electrode with spatially combined heating zones.

#### Sixth order linear differential equations using GeoGebra applets

Jorge Olivares1 , Germain Pastén2 , Jonnathan Rodríguez3

###### Abstract

This paper presents a way to visualize the solutions of sixth order linear differential equations using GeoGebra software. The representation of the solutions of this type of equations will be visualized using GeoGebra applets, which will dynamically allow understanding of the graphical behavior of the algebraic solutions contributing with a tool in the development of meaningful learning for the students in this topic.

#### Impact of Chest Radiograph Image Size and Augmentation on Estimating Pulmonary Artery Wedge Pressure by Regression Convolutional Neural Network

Yuto Omae1 , Yuki Saito2 , Daisuke Fukamachi3 , Koichi Nagashima4 , Yasuo Okumura5 , Jun Toyotani6

1Nihon University, College of Industrial Technology, Japan
2Nihon University, Department of Medicine, Japan
3Nihon University, Department of Medicine, Japan
4Nihon University, Department of Medicine, Japan
5Nihon University, Department of Medicine, Japan
6Nihon University, College of Industrial Technology, Japan

###### Abstract

Heart failure is related to pulmonary artery wedge pressure (PAWP), which is one of the measurements for diagnosing heart disease. In the case of suspected heart failure, it is desirable to measure PAWP by right heart catheterization (RHC). However, RHC is an invasive procedure accompanied with the risk of complication. Therefore, a method to quantitatively estimate PAWP from chest radiographs by a regression convolutional neural network (R-CNN) was proposed as the previous study. The risk of complication is eliminated because the method is non-invasive. Moreover, developed R-CNN include regression activation map (R-AM), which is one of the white-box techniques for CNN. However, tuning hyper parameters of R-CNN (e.g., input image size and data augmentation) developed in previous researches, is insufficient. Therefore, we carry out sensitivity analyses of input image sizes and data augmentation against estimating PAWP from chest radiographs. Through these analyses, we found the appropriate input image size and data augmentation.

#### Loewner dynamics of anomalous diffusion and turbulence phenomenon

Yusuke Shibasaki1

1Nihon University, Department of Correlative Study in Physics and Chemistry, Graduate School of Integrated Basic Sciences, Japan

###### Abstract

The stochastic Loewner evolution (SLE) is a widely acceptable model for conformally invariant random curves generally encountered in the two-dimensional (2D) statistical mechanics models. Although its efficacy in describing the static 2D morphology has been demonstrated in numerous studies, the dynamic properties of the SLE curve growth lack the required clarity because of the problems associated with time in the Loewner differential equation. Physically, it is expressed using the dimension of space and is sometimes referred to as the Loewner time. It has a unique scaling property which is different from the usual sense of physical time. Exploiting this property, the author in a recent study suggested a transformation method for converting the Loewner time to physical time and vice versa. In the present study, we investigate the physical property related to the SLE curve dynamics post the Loewner time transformation and discuss it in context of the turbulence phenomenon. We demonstrate that the dynamics of the SLE curve in physical time $x(t)$ can be modeled as a one-dimensional anomalous diffusion process with variance of ${\langle x(t) ^2\rangle}\sim{t^3}$. This scaling law is independent of the main parameter $\kappa$ of the SLE. Further, it corresponds to the Richardson’s law of the relative dispersion of the particles, which is a fundamental law of turbulence theory. We anticipate that the modifications to the driving function of the Loewner evolution (like applying chaotic diffusion processes) will provide additional details about the turbulence phenomenon.

#### Geometrical Properties of Leaf Apex and its Effect on Water Drainage Ability

Rachanonphos Thananonthasawat1 , Apisara Comchiang2 , Chayanant Sandee3 , Pimsiri Danphitsanuparn4 , Pat Vatiwutipong5

4Kamnoetvidya Science Academy, Biology and Environmental Science, Thailand
5Kamnoetvidya Science Academy, Mathematics and Computer Science, Thailand

###### Abstract

Water drainage is a vital mechanism for plants. Plants adapt their leaves to survive. The drip tip, the elongate leaf tip, is an example of plant adaptation to the high rainfall areas. Water is removed at the drip tip to avoid rotten leaves. This character helps plants drain the water from the leaf surface and protect against leaf damage. This study focuses on the relationship between leaf apex shape and water drainage ability. Lagerstroemia sp. is selected in our research. Leaves were collected and flattened by using a plant press and heat. The water was dropped on the leaf. The drained water was weighted, and then calculated the leftover water on the leaf surface. The drip tip pictures were analyzed. A mathematical model was also created to find an equation describing the shape of the leaf apex. The different leaf apex shapes affected water drainage ability. Following the previous study, the narrower angle had a higher water drainage ability. The results showed a strong correlation between the water drainage ability and our model parameters.

#### The Core-Mantle Boundary velocity field in the recent decades

Klaudio Peqini1 , Elisabeta Koçi2 , Dode Prenga3 , Rudina Osmanaj4

1University of Tirana, Department of Physics, Albania
2Faculty of Natural Sciences, University of Tirana, , Albania
3University of Tirana, Department of Physics, Albania
4Faculty of Natural Sciences, University of Tirana, , Albania

###### Abstract

The fluid motion in the Earth's outer core is usually considered an almost ideal conductor. Its convective motion is theoretically, experimentally and numerically found to be the mechanism which generates and maintains the internal magnetic field. Using the induction equation it is possible to infer the velocity field at the boundary between the outer core and the lower mantle (known as Core-Mantle Boundary, CMB). In the literature are reported multiple cases where one can make use of either the existing data from a myriad of geomagnetic observatories, or the set of Gauss coefficients from existing geomagnetic models. In the present paper we use the CHAOS field model which spans the last decades (1999 - 2020), thus enabling us to calculate the velocity field for the satellite observation era. Many of the important features observed for the geomagnetic can be explained by analyzing the respective CMB velocity field.

#### Strong cosmic censorship theorem in Bakry-Emery spacetimes

Makoto Narita1

1National Institute of Technology, Okinawa College, Department of Integrated Arts and Science, Japan

###### Abstract

A class of naked strong curvature singularities is ruled out in Bakry-Emery spacetimes by using techniques of differential topology in Lorentzian manifolds. These spacetimes admit a Bakry-Emery-Ricci tensor which is a generalization of the Ricci tensor. This result supports to validity of Penrose's strong cosmic censorship conjecture in scalar-tensor gravitational theories, which include dilaton gravity and Brans-Dicke theory.

#### Mathematical Modeling of Oil and Gas Kick during Drilling Operations

Fotios Zachopoulos1 , Nikolaos Kokkinos2

1International Hellenic Univeristy, Chemistry, Greece
2International Hellenic University, Department of Chemistry, Greece

###### Abstract

Τhe current study aims to provide the modern available techniques to mathematically describe and model a potentially disastrous event, called “kick”. A kick might occur during drilling for oil and gas and it is defined as the unscheduled influx of formation or reservoir fluids into the wellbore. If the kick is not early detected or properly mitigated, a blowout might occur. To improve the respective detection and mitigation methodologies, the kick must be accurately simulated. The PRISMA reporting system was employed, to systematically review the current literature and the available modeling techniques and mathematical models. Cubic equations of states (EOS), such as Peng-Robinson with Van der Waals mixing rules and binary interaction coefficients, are used to describe the thermodynamic state of the kick. In addition, semi-empirical mathematical models are also considered to account for factors affecting the behavior of kick, such as the compressibility, the friction in annular space, the heat-transfer effects, the solubility of fluids in drilling mud, the changes in bottom hole pressure and the gas bubble rise velocity. Usually, when such a simulation is performed, several of the aforementioned factors are ignored or oversimplified. Furthermore, studies are usually conducted under several assumptions that might lead to compromised results and inaccurate modeling of the dynamic behavior of the fluid’s multiphase flow. A modern approach using computational fluid dynamics (CFD) was examined and evaluated, as the mean to simulate the flow of a kick in the actual geometry of a well. Navier-Stokes differential equations are also presented in conjunction with CFD to describe the motion of the fluid by taking into account the conservation of momentum and mass. Finally, the study results to a proposed methodology of modeling a hydrocarbon kick by combining the existed mathematical models and equations with the power of modern techniques such as computational fluid dynamics.

#### COMPUTER 3D MODELING BIOORGANIC COMPOUNDS: HOW THE AMINO ACIDS CAN BE CREATED?

Volodymyr Maslyuk1

1Institute of Electron Physics, Photonuclear processes' , Ukraine

###### Abstract

The paper presents the results of structural modeling of bioorganic compounds of C, H, N, and O atoms by the common formula CxHyNzO1-x-y-z. The ball-and-stick approximation was used to analyze significant arrays of their homo- and hetero- bonds switching. Model calculations have used the method of structural combinations and color statistics, which considers the statistical inequality of atoms of biomolecules with different binding energies. It all allows us to estimate the degeneracy of the biomolecule by the number of structural statesto find the configuration entropy and information capacity.Thus, the calculations give the value of 40-50 bits of the information capacity for a typical amino acid. The results of structural modeling for all amino acids are presented, and the general set of color nets, common for all of them, is established. The results of using the Unity package for 3D graphic simulation of the structure of bioorganic compounds as a structural graph for each color set are presented. Methods of 3D visualization of simulation results, filtering algorithm, and graph construction optimization are discussed. The main point of this research work is to outline and strictly describe the question of the exclusivity of the class of amino acids among bioorganic molecules of similar atomic compositions, taking into account their entropy and energy parameters.

#### Calculations on a new endohedral: CH4@C60

Zdenek Slanina1

1University of Arizona, Department of Chemistry and Biochemistry, United States

###### Abstract

Recently, a new non-metal fullerene endohedral has been prepared, namely CH4@C60 [S. Bloodworth et al., First Synthesis and Characterization of CH4@C60, Angew. Chem. Int. Ed. 58 (2019) 5038]. In this report, its computational characterization is presented (structure, energetics, spectra). The methane encapsulation into C60 is evaluated using the DFT (M06-2X functional) and B2PLYPD as well MP2 correlated treatments with the standard 6-31++G** basis set, enhanced with the basis set superposition error (BSSE) estimated by the Boys-Bernardi counterpoise (CP2) method. The static symmetry of the endohedral obtained from the geometry optimizations is T. The CH4 encapsulation is attractive, yielding a substantial energy gain of about 12.5 kcal/mol when evaluated at the most advanced level, B2PLYPD=FU/6-31++G**. Such encapsulation energy could allow for the high-temperature and high pressure synthesis. The calculated structural characteristics and IR vibrational spectrum are presented, too.

#### On the calculation of correlation functions for organic solvents: comparison of RISM and MD approaches

1Cherepovets State University (CHSU), Laboratory of Mathematical and Computer Modelling of Nanostructures, Russian Federation

###### Abstract

The long-term performance of lithium-ion batteries is influenced by the mechanical stability of their polymer separators. The experimental studies [1, 2] show that swelling in electrolyte solvent affects the mechanical properties of the separators. Because the mechanical failure of the separators can cause a short circuit, the ability to predict the mechanical properties of the polymer porous membrane in electrolyte solvents has great importance for developing new separator materials. MC\RISM approach [3] which combines Monte Carlo simulation and numerical solving RISM (reference interaction site model) integral equation has been proved to be effective for studying the polymer solutions. In this work, we make the first step to developing the predictive tool for estimating the mechanical properties of porous polymers in electrolyte solvents. In order to apply MC\RISM method, it needs to calculate the intermolecular correlation functions for organic solvents. To obtain these functions, we applied two different approaches: numerical solution of RISM integral equations and molecular dynamics (MD) method. The correlation functions were calculated for several organic solvents (acetone, diethyl carbonate, ethyl acetate). We found that the results of both RISM and MD methods are in a good agreement. [1] Gor, Gennady Y., et al. "Swelling and softening of lithium-ion battery separators in electrolyte solvents." Journal of Power Sources 294 (2015): 167-172. [2] Yan, Shutian, et al. "Unveiling the environment-dependent mechanical properties of porous polypropylene separators." Polymer 55.24 (2014): 6282-6292. [3] Khalatur, Pavel G., and Alexei R. Khokhlov. "Hybrid MC/RISM technique for simulation of polymer solutions: Monte Carlo+ RISM integral equations." Molecular Physics 93.4 (1998): 555-572

#### Molecular dynamics sampling scheme utilizing dynamically enforced heat-bath temperature

Ikuo Fukuda1 , Kei Moritsugu2

1University of Hyogo, Graduate School of Information Science, Japan
2Osaka Metropolitan University, , Japan

###### Abstract

Molecular dynamics (MD) is widely used in chemical, biological, material physics to investigate characteristics of physical systems in terms of their microscopic descriptions. Although an approach to produce the Boltzmann–Gibbs distribution connecting experiments and the MD simulations has been studied, it is still hard to fully sample the phase space spanned by the coordinate variables describing the physical system. Here we developed an MD scheme represented by an ordinary differential equation that generates a distribution defined by the Boltzmann–Gibbs density along with a weight function of a heat-bath inverse temperature, which is treated as a dynamical variable. The scheme handles the inverse temperature as a combination of multidimensional dynamical variables and enhances the fluctuations to enforce the phase-space exploration. Specific protocols of the scheme and its characteristic features are presented.

#### Parallel Algorithm For Modeling Of Internal Ballistics In Solid Rocket Motors

Damian Kaniewski1

1Łukasiewicz Research Network - Institute of Aviation, Space Technologies Center, Poland

###### Abstract

Simulation of a solid rocket motor (SRM) operation in terms of the internal ballistics (IB) analysis can be approached in many different ways. The most popular 0D quasi-steady-state analytical methods though being very fast, are usually limited to fairly simple propellant geometries and preliminary analyses. Complex propellant shapes pose significant problem associated with accurate surface burnback representation. In recent years Level-Set Method (LSM) has been shown as the most universal technique for this application, because it handles any kind of isosurface evolution including topology changes. This method allows also to apply non-isotropic burning rate models, and therefore recreate accurate representation of burning surface regression. However, LSM’s major drawback is associated to the computational cost which grows in exponential rate with increasing grid resolution. Fortunately LSM is vulnerable to parallelization to high extent and such approach can give enormous speedup in calculations. This paper presents the benefits that can be achieved using CUDA architecture in large numerical simulations concerning the internal ballistics of SRMs. Paper presents also possible multiphysics model integration which includes simulation of flow, deformation and heat transfer.

#### Emergence of effective Lorentzian metric from a vortex defect

Alice Roitberg1

1Università di Milano Bicocca, Matematica e Applicazioni, Italy

###### Abstract

By applying standard linearization techniques to the hydrodynamic formulation of the Gross-Pitaevskii equation governing a Bose-Einstein condensate I prove that certain invertibility conditions are satisfied when we consider the simple case of a steady, straight vortex defect. This result has important implications in the study of cosmological analogue models in black hole theory, because it allows to derive an effective Lorentzian metric that governs phononic perturbations.

#### The Generalizized Gauss Principal Application For Oscillations Suppression Of A Cart With Triple Rods Pendulum

Mikhail Yushkov1 , Sergei Bondarenko2

1Saint Petersburg State University, The theoretical and applied mechanics department, Russia
2Saint Petersburg State University, The theoretical and applied mechanics department, Russian Federation

###### Abstract

The problem of oscillations suppression of a cart with triple rods pendulum is observed. The oscillations are appeared due the rest-to-rest movement of the system. At first, the problem was considered as the control problem and solution was found from Pontryagin maximum principal. Than high order nonholonomic bond was discovered. The bond is fulfilled for all movement time. After that another solution was gained by nonholonomic mechanic method --- generalized Gauss principal. The solutions are compared graphicly. For the long-time movement the second principal had more smooth behavior. For the short-time movement the boundary-value problem was extended. This helped to eliminate the first two solutions defect --- the force jumps at starting and ending times.

#### Stability Analysis and the DRBEM Solution of the Unsteady MHD Slip Flow Problem

Pelin Senel1

1Karadeniz Technical University, Department of Mathematics, Turkey

###### Abstract

In this study, the unsteady Magnetohydrodynamics (MHD) slip flow in a square cavity subjected to a uniform horizontal magnetic field is investigated. The coupled time-dependent MHD equations with the slipping velocity and the insulated wall conditions are discretized by the dual reciprocity boundary element method (DRBEM). The resultant algebraic equations are rearranged containing both the velocity and the induced magnetic field unknowns and their normal derivatives. The time is discretized by the explicit Euler method. The numerical stability analysis is carried through the spectral radius of the final coefficient matrix. The choices of the relaxation parameters and the time steps for the problem constants are discussed. The steady state flow behaviors for various slip lengths, Hartmann ($Ha$), Reynolds ($Re$) and magnetic Reynolds ($Rm$) numbers combinations are presented. It is found that, for fixed $Ha$, slip length, relaxation parameters and time step, the spectral radius of the coefficient matrix increases as $Re$ or $Rm$ advances. Large time steps and the relaxation parameters close to one give numerically stable results. The slip on the walls accelerates the flow, thickens the side layers and shrinks the Hartmann layers. Increasing $Ha$ or $Re$ decelerates the flow. The DRBEM is capable of giving numerically stable results for the MHD slip flow problem with a less computational cost due to its boundary only discretization nature.

#### Heat transfer modeling in road lighting LED luminaire

Carlos Velásquez1

1University of Alicante, Dept. of Applied Mathematics, Ecuador

###### Abstract

Efficient lighting is a goal for energy efficiency and sustainable development. There are designs for electrically powered public lighting fixtures with solar panels installed in hard-to-reach areas or protected areas without an electrical power supply network. In this paper, a LED luminaire has been modeled by solving the heat equation using a heat source (LED 50W) to observe its behavior. The simulations were developed at ambient temperatures of 24°C and 35°C. It is important because these luminaires are installed in areas with this usual temperature, for example, the Ecuadorian Amazon or the Galapagos Islands. 51.7°C was obtained in LED for an ambient temperature of 24°C, which is the normal laboratory case, and 62.5°C in LED for an ambient temperature of 35°C. These results must be analyzed since it has a direct impact on the expected life of the luminaire and therefore on the maintenance and replacement plans. Through the results obtained, it was determined by Arrhenius model a reduction of 160 days in the maintenance plan.

#### Study of transient wave and vibro-acoustic response of a cymbal during laser impact via FEM-BEM numerical simulations

Evaggelos Kaselouris1 , Vasilis Dimitriou2

1Hellenic Mediterranean University, Department of Music Technology and Acoustics, Rethymnon, Greece
2Hellenic Mediterranean University, Department of Music Technology and Acoustics, Rethymnon, Greece

###### Abstract

The transient wave and vibro-acoustic response of a cymbal is studied when irradiated by a pulsed ruby laser via time domain finite element method - boundary element method numerical simulations [1,2]. The cymbal is modeled with finite elements while the air environment is modeled with boundary elements. The radiated sound due to the impact can be computed at any point of the air solution domain. The equivalent surface load corresponding to the laser pulse is used as a loading condition [3]. The first observable bending waves reach the edge of the cymbal in approximately 50 ms. These waves are followed by waves of longer wavelength which due to reflection effects at the central dome result to the generation of standing waves. The simulation results agree well with literature experimental results in a study of the transient wave response of a cymbal using double-pulsed TV holography [4]. 1. E. Kaselouris, C. Alexandraki, M. Bakarezos, M. Tatarakis, N. A. Papadogiannis, V. Dimitriou, Int. J. Circuits Syst. Signal Process 16, 948-955 (2022). 2. E. Kaselouris, C. Alexandraki, Y. Orphanos, M. Bakarezos, M. Tatarakis, N. A Papadogiannis, V. Dimitriou, INTER-NOISE and NOISE-CON Congress and Conference Proceedings 263, 3378-3385 (2021). 3. Y. Zhan, C. Liu, X. Kong, Z. Lin, Ultrasonics, 73, 271-276 (2017). 4. S. Schedin, P. O. Gren, T. D. Rossing, J. Acoust. Soc. Am. 103, 1217-1220 (1998).

#### BELL-SHAPED WAVE THEORY FORMATION ANDMATHEMATICAL CONCERT SIMULATION FOR HYDROLOGICALLY PULSATING FLOW ON INDUCED MAGNETIC FIELD IN A POROUS MEDIUM

CHIDAMBARAM LA ,1

1ANNAMALAI UNIVERSITY, MECHANICAL ENGINEERING, FACULTY FOR ENGINEERING & TECHNOLOGY, India

###### Abstract

Authors: Elangovan K* and Chidambaram LA** *-Mathematics Section, Faculty for Engineering & Technology, Annamalai University, Chidambaram- 608 001, India **-Mechanical Engineering, Faculty for Engineering & Technology, Annamalai University, Chidambaram-608001, India Corresponding author: lakshchidambara@yahoo.com ABSTRACT The Bell- shaped wave theory formation for considered fluid flow in Human structure has been elaborated in this research article, in addition to mathematical performance that is simulated through solution formation for pulsating hydrological flow in a porous medium through an externally induced magnetic field. A comprehensive study, focusing on the Fluid flow axis-symmetry channels have been experimented on for pulsating flow fluid analysis, where expressions are arrived at for axial velocity, volume flow rate and the pumping phenomenon which shows a pressure gradient that plays an important role even while the heat is exchanged from Humans. Living with sustainable time intervals uninterruptedly. Extensive literature investigations show that, while a Magnetic influence is Larger, the fluid flows occur faster in the linear axis symmetric fluid channels and with non-influence or little influence the wave formations are lesser in a considered flow as in a hydrological peristaltic fixed frame wave length conditions. Key Words: Magnetic Field, Hydrological Flow, Coupled stress model, Peristalsis/Pulsating, Pumping power

###### Acknowledgements:

The Authors thank World Scientist "Prof.R.Velraj", Vice-Chancellor, Anna University, Tamil Nadu for his virtual research mentoring in scripting this article and further this article insights from "Prof.S.Palaniappan and Prof V.R.Muthuveerapan" Former Head-Mechanical, Department of Engineering, Annamalai University with thankful appreciations and, further the authors also acknowledge all the authors quoted as references with their scholarly articles

#### Expected number of fingers in the radial displacement of confined viscous fluids

Rafael Oliveira1 , Larissa Santos2 , Pedro Câmara3

1Pontifical Catholic University of Rio de Janeiro, Mechanical Engineering, Brazil
2Pontifical Catholic University of Rio de Janeiro, Mechanical Engineering, Brazil
3Pontifical Catholic University of Rio de Janeiro, Mechanical Engineering, Brazil

###### Abstract

We conduct linear stability analysis and nonlinear simulations based on a boundary integral method with small-scale decomposition to investigate the radial displacement of viscous fluids in the confined environment of a Hele-Shaw cell. The linear analysis is known to predict the fastest growing mode, which is related to the expected number of fingers. The nonlinear regime of this displacement process is known to produce tip-splitting events that ultimately will determine the number of fingers. We conduct high resolution numerical simulations varying the two dimensionless parameters that control the dynamics, namely the viscosity contrast and the effective surface tension, to examine the nonlinear stages of cases in which the linear analysis predict the same time evolution for the fastest growing mode. The evolution of the number of fingers produced by the nonlinear simulations differs significantly from the linear expectations. In addition, the results produce visually striking interfacial patterns.

###### Acknowledgements:

We thank Human Resources Program of the Brazilian National Petroleum Agency (PRH-ANP) for financial support.

#### On the role of quantum superpotentials in the position dependent mass Schrödinger equation

Gerardo Ovando1 , Juan Peña2 , Jesús Morales3 , José López-Bonilla4

1UNIVERSIDAD AUTÓNOMA METROPOLITANA - AZC, Ciencias Básicas - FAMA, Mexico
2UNIVERSIDAD AUTÓNOMA METROPOLITANA, CIENCIAS BÁSICAAS, Mexico
3UNIVERSIDAD AUTÓNOMA METROPOLITANA, CIENCIAS BÁSICAS, Mexico
4INSTITUTO POLITÉCNICO NACIONAL, ESIME-ZACATENCO, Mexico

###### Abstract

The von Roos’ position dependent mass Schrödinger Equation (PDMSE) is given in terms of an effective potential where, in addition to the potential under study, includes a term that takes into account ambiguity parameters. At this regard, some of the most important approaches to the ambiguity parameters are those of BenDaniel-Duke, Gora-Williams, Zhu-Kroemer, Li-Kuhn and so on. In this work we show that for the cases of Zhu-Kroemer and BenDaniel-Duke it is possible to express any solvable potential through a pair of quantum superpotentials. To this, we stablish the factorization of the PDMSE Hamiltonian and the use of a point canonical transformation that allow to identify a first superpotential $W(x)$. Next, the term in the effective potential with ambiguity parameters is expressed through a function $Z(x)$ and the cases when $Z(x)$ is a quantum superpotential are discussed. In this form, the proposed superpotentials determine the solvable potentials in the PDMSE, the energy spectra and mass functions. We give some examples to explain the approach which can be straightforwardly applied to the solution of the PDMSE for other different potential models and mass distributions.

#### Computer Simulation of Fractal Patterns in Polymer Electrolyte Films via Application of Fractal Growth Parameters

Shahizat Amir1

1UNIVERSITI MALAYA, MATHEMATICS, Malaysia

###### Abstract

Polymer electrolyte films have been reported to grow fractal patterns and simulations of these fractal patterns have been done. In this work, Diffusion limited aggregation (DLA) model of fractal growth was integrated with Brownian motion theory in the computer simulations of fractal patterns in polymer electrolyte films via application of fractal growth parameters. Growth rules along with major properties of the model were demonstrated. Computer simulation of the model applying fractal growth parameters extending their sticking coefficients, number of particles and lattice sites was performed on the platform of Matlab version 7.12. With the change of the growth parameters, noticeable differences in the simulation results were obtained. The fractal dimensions, D of the fractal patterns obtained from experimental and simulation work were calculated using the box-counting method. The effects of different growth parameters on fractal dimension were also discussed here.

#### SPIN SYSTEMS ASSOCIATED WITH INTEGRABLE NONLINEAR SCHROEDINGER EQUATIONS

Kuralay Yesmakhanova 1 , Ainur Zhumageldina2 , Akgul Naizagarayaeva3

1Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics, L.N. Gumilyov Eurasian National University, Department of General and Theoretical Physics, Kazakhstan
2L.N. Gumilyov Eurasian National University, Department of General and Theoretical Physics, Kazakhstan
3Saken Seifullin Kazakh Agro Technical University, , Kazakhstan

###### Abstract

In the theory of solitons, the notion of gauge equivalence between different nonlinear equations plays an important role. The system of nonlinear Schrödinger equations is integrable. In this work, we consider the gauge equivalence between (2+1) - dimensional nonlinear Schrödinger type equations and their spin systems. As often happens, we have some spin system for which we do not know the Lax representation or any other properties indicating its integrability or non-integrability. In this case, the gauge equivalence method does not work. However, it is still possible to find a non-linear equation equivalent to a given spin system using the concept of the so-called L-equivalence (Lakshmanan equivalence). This approach uses a number of equations from the theory of curves and surfaces from differential geometry. In this case, for example, the Gauss–Codazzi–Mainardi equation from the theory of surfaces is the very nonlinear equation that is equivalent to a given spin system. In this paper, we consider a number of spin systems related to nonlinear Schrödinger equations or their reductions.

###### Acknowledgements:

This work was supported by the Ministry of Education and Science of Kazakhstan under grants AP08856912.

#### Finding chaos in cardiac electrophysiology

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

###### Abstract

Cardiac arrhythmias are the collective term for heart rhythm disorders. These diseases also include cardiac fibrillation, characterized by the chaotic propagation of electrical signals in cardiac tissue. This work is devoted to detecting chaotic cardiac cell responses that could cause this chaotic propagation. For this purpose, mathematical models of the heart cell are used, which are stimulated by a current with various amplitudes and frequencies. The responses of these models are investigated using modern and classical methods of dynamic systems such as the 0-1 test for chaos, recurrence quantification analysis, entropy calculation, etc. Thanks to these methods, the cardiac cell pacing current parameters, which cause chaotic and regular responses, are revealed.

###### Acknowledgements:

This work was supported by The Ministry of Education, Youth and Sports from the Large Infrastructures for Research, Experimental Development, and Innovations project "e-INFRA CZ - LM2018140".

#### An inverse model for the peeling-based recovery of unitary layers from laminated structures

Moritz Becker1 , Mathieu Imbert2 , Michael May3

1Fraunhofer Institute for High-Speed Dynamics, Ernst-Mach-Institut, EMI, Materials and Simulation Methods, Germany
2Fraunhofer Institute for High-Speed Dynamics, Ernst-Mach-Institut, EMI, Materials and Simulation Methods, Germany
3Fraunhofer Institute for High-Speed Dynamics, Ernst-Mach-Institut, EMI, Materials and Simulation Methods, Germany

###### Abstract

The recycling of composite materials is a major challenge as it is systematically associated, in classical processes, with a downcycling due to the reduction of the fiber length. However, recent works demonstrated that the recovery of the unitary layers of laminated structures with preserved mechanical properties is possible under dedicated loading conditions. This requires that the fibrous reinforcement is not damaged during the peeling recovery process. An innovative inverse numerical model is proposed, which enables to directly compute the magnitude and orientation of the loads leading to layer separation without damaging the fibrous reinforcement. Separation of the peeled layer from the substrate is modelled using a discretized two-layer model with cohesive zone described by a set of equations which is solved numerically. Different approaches are finally proposed to take into account the bending-induced damage of the peeled layer, in order to realize accurate predictions even in the cases in which damage cannot be avoided.

###### Acknowledgements:

The authors acknowledge the Leistungszentrum Nachhaltigkeit Freiburg for the financial support in the frame of the project MultiTrace.

#### HIROTA AND MAXWELL-BLOCH'S LOCAL NONLINEAR EQUATION: DARBU TRANSFORMATION AND SOLUTION.

Assel Zhamysheva1 , Kuralay Yesmakhanova 2

1L.N. Gumilyov Eurasian National University, Nur-Sultan, Kazakhstan. Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics, Nur-Sultan, Kazakhstan,, Faculty of Physics and Technology, Kazakhstan
2Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics, L.N. Gumilyov Eurasian National University, Department of General and Theoretical Physics, Kazakhstan

###### Abstract

Integrable equations are widely used as models for explaining physical phenomena in many fields of science, such as plasma physics, Liquid Mechanics, solid state physics, optical fibers, and Chemical Physics. Currently, many theoretical works pay more attention to the practical implementation of integrable equations. One of the most important systems implemented in practice is the related system of the Hirota equations and Maxwell-Bloch equations (MB). In this work, inspired by the ideas of muslimani and Ablowitz, we successfully obtained local nonlinear equations of Hirota and Maxwell-Bloch (Hirota-MB). The formulation of the lax pair for the nonlinear Hirota-MB equation is proposed, in which the offset consists of the inverse time field in nonlinear local terms. A detailed proof of the Darbu transformation for this equation is given. His decision was made through the transformation of Darb. The idea behind the non-local symmetry method is to establish the relationship between local equations and the corresponding non-local equations, choosing the appropriate symmetry to study their properties and solutions. Among the forms of symmetry, there are many differences in the relationship between time and space between these non-local and local equations, new physical phenomena can occur, and new physical applications can be created. It is also possible to obtain similar types of N-order solutions with a spectral parameter, being the image of lax.

#### Obtaining Schenberg detector frequencies antenna under gravity and misalignment using finite element modeling

Carlos Frajuca1

1FURG, IMEF, Brazil

###### Abstract

The resonant-mass gravitational wave detector SCHENBERG is a spherical detector that will operate with a central frequency around 3200 Hz with a bandwidth of 100 to 200 Hz. It has a spherical mass that works as an antenna that weighs 1150 kg and is connected to the outer environment by a suspension system designed to attenuate local noise due to seismic as well as other sources of vibration. The sphere is suspended by its center of mass. When a gravitational wave passes by the detector, the antenna is expected to vibrate; this motion is monitored by six parametric microwave transducers whose output signals are digitally analyzed. In order to determine the detector performance better, it is necessary to obtain the vibration frequencies of the sphere with a better precision. To achieve such a goal the sphere with the holes to mount the transducers and the central hole from which the sphere is suspended is simulated in a finite element method program when the gravity is applied to the sphere and the deformation is kept. After that the vibration normal modes of the sphere are calculated and they are compared to the experimental results. After that the gravity is misaligned with the suspension of the sphere to simulate the effects of it, then the simulation is done again and no differences were found.

###### Acknowledgements:

CF acknowledges FAPESP (Brazil) for grants #2013/26258-4 and #2006/56041-3 as well as CNPq for grant 309098/2017-3.

#### Second optimization stage of a composite quadrupole mass at high-speed rotation

Carlos Frajuca1

1FURG, IMEF, Brazil

###### Abstract

This work shows the optimization process of a quadrupole mass at high-speed rotation using the finite element modeling (FEM). Such a mass should compose a gravitational signal generator device, which is intended to use in an experiment to measure the speed of gravity. The device must produce a tidal gravitational signal with a frequency of 3200 Hz. The gravitational wave detector Mario Schenberg is the first option as the detector of the signal. The previous steps of the project are briefly discussed, and the FEM simulations for the quadrupole mass are shown. An analysis of the mechanical stresses produced at high-speed rotation is presented. The most successful 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.

###### Acknowledgements:

CF acknowledges CNPq for grant #309098/2017-3 and #312454/2021 and FAPESP (Brazil) for grants #2013/26258-4 and #2006/56041-3.

#### Optimization of a Flywheel Electromechanical Battery Rotor Geometry for Improving the Energy Density

Carlos Frajuca1

1FURG, IMEF, Brazil

###### Abstract

This work presents a specific mechanical device known as Flywheel, capable of storing kinetic energy due its high rotational speed. This device is also known as an electromechanical battery. Compared to other commercial batteries, batteries containing Flywheels have longer lifetime, are less potentially damaging to the environment and have high power output. The aim here is to analyse the behaviour of flywheels rotating at the highest possible tangential speed, thus concentrating more energy, with changes in the flywheel geometry with the objective to minimize material costs, as the material to be used in their construction in the future, CarbonNanoTubes for instance, is a very expensive material. The commercial software SolidWorks was used for geometry analysis of the flywheel rotor to obtain the von Mises stress under rotation. Based on the model suggested previously the Finite Element Method was used to create and simulate inertial flywheel models with different geometries. These models gradually incorporated successive geometry changes for the increase of tangential speed. After seeking an initial dimension through the research of rotor geometry. The material chosen for the simulations was a commercial carbon fiber. The material used presents characteristics that can support the high stress to which the rotor is subjected. The analysis indicated a geometry that allows the best performance for the development of a flywheel with the lowest cost and high yield showing a very homogeneous distribution of the von Mises stress all over the flywheel structure.

###### Acknowledgements:

CF acknowledges CNPq for grant #309098/2017-3 and #312454/2021 and FAPESP (Brazil) for grants #2013/26258-4 and #2006/56041-3.

#### Multistability of models with infinite equilibria

Judita Buchlovska Nagyova1

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

###### Abstract

The main aim of this paper is to analyze the multistability of models with infinite equilibrium points. The corresponding three-variable models are given as a set of nonlinear ordinary differential equations containing a non-smooth function. The coexistence of multiple attractors is studied depending on the parameters and the initial condition of the system. For this purpose, the parameters and initial conditions are perturbed and periodic orbits are found close to the chaotic attractor using Newton's method.

#### A Theoretical Analysis of CuVX2 (X = S, Se, Te) in reference to Photovoltaic Application

Saloni .1

1Sharda University, Department of Chemistry, India

###### Abstract

Addressing the issues related to energy demand is one of the challenging scientific research domains. A number of scientists have been working on this issue since long back and trying to find the suitable photovoltaic materials which provide better performance and efficiency. Ternary chalcopyrite-type materials have shown a great potential application for light emitting diodes, solar cells, and photocatalysis due to their unique electronic and optical properties. In this report, ternary chalcopyrite-type materials CuVX2 (X = S, Se, Te) are studied by using Conceptual Density Functional Theory (CDFT) approach. Geometry optimization is performed through exchange correlation LSDA and basis set LANL2DZ within Density Functional Theory framework. The optimized structures of CuVX2 show real vibrational frequencies. The computed HOMO-LUMO energy gap signifies that these chalcopyrite materials can be suitable for photovoltaic applications. CDFT based descriptors – vertical ionization potential, vertical electron affinity, chemical hardness, softness, electronegativity, electrophilicity index and dipole moment of CuVX2 are calculated and analyzed. An interesting correlation is observed between HOMO-LUMO energy gap and CDFT based descriptors of CuVX2 materials. The calculated bond length is in line with the experimental data.

#### Reduction of degrees of freedom for large scale systems in computer assisted proofs

Oleg Ryabkov1 , Nikolay Evstigneev2

1Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow, Russia, Macrodynamic systems, Russia
2Federal Research Center ''Computer Science and Control'' of the Russian Academy of Sciences, Macrodynamic systems, Russian Federation

###### Abstract

In many physical systems, it is important to know the exact trajectory of the solution. Such applications include celestial mechanics, fluid mechanics, robotics, etc. For cases where analytical methods cannot be applied, one can use computer-assisted proofs or rigorous computations. One can obtain a guaranteed bound for the solution trajectory in the phase space. The application of rigorous computations poses few problems for low-dimensional systems of ODEs but is a challenging problem for large scale systems, for example, systems of ODEs obtained from the discretization of the PDEs. We are interested in the application of rigorous computations to the problem of proving the existence of a periodic orbit in the Kolmogorov problem for the Navier-Stokes equations. One of the key issues, among others, is the computation complexity, which increases rapidly with the growth of the problem dimension. This is the problem that we intend to address in this paper. The system is described by the discrete set of ODEs on variable $w$: $$(w_{j,k})_t=-R^{-1}(4 j^2+k^2) w_{j,k} + \delta_2^{|k|}+\mathcal{B}(w),$$ for all $\{j,k\} \in [2 M \times M]$. Here $M$ is a finite integer, $\mathcal{B}(w)$ is a convolution nonlinear term, $w$ represents curl of the velocity field, $\delta$ is the Kronecker delta and $R$ is the parameter (Reynolds number). The system under consideration is obtained from the Galerkin approximation of the Kolmogorov problem. In the previous papers, we showed that $M \geq 10$ is needed on order to achieve convergence of the rigorous algorithm. Here we wish to demonstrate the application of the proper orthogonal decomposition in order to approximate the attracting set of the system and reduce the dimension of the active degrees of freedom. This allows one to accelerate the process of obtaining rigorous bounds and consider problems of larger scale.

#### Mathematical model for the rate of heat transfer through a single droplet

Dimitrios Perros1 , Christos Nikolopoulos2 , Vassilis Stathopoulos3

1National and Kapodistrian University of Athens, General, Greece
2University of the Aegean, Mathematics, Greece
3National and Kapodistrian University of Athens, Laboratory of Chemistry and Materials Technology, Department of Agricultural Development, Agrofood and Management of Natural Resources, Greece

###### Abstract

The dropwise condensation is of major importance with a decisive contribution to a wide range of industrial applications, such as heat transfer, antifrosting and self-cleaning. A first step in this process is to understand the basic mechanisms of condensation and heat transfer in a single drop. In this paper an attempt is made to describe this process through a mathematical model. This model takes into account mass conservation as well as heat transfer, in the transient phase change between vapor-liquid. Due to the small size of the droplet, it is considered that the heat is transferred both at the border and inside only with conduction. Due to the spherical shape of the droplet, spherical coordinates were chosen for the equations. Initially in the heat equation it was assumed that only the radius r of the spherical coordinates changes and that the droplet maintains its spherical shape until it reaches the maximum radius of removal from the substrate. The model was then enriched by changing the polar angle θ, assuming that the droplet during condensation is a hemisphere. The simulation results are compared with experimental data.

###### Acknowledgements:

The project leading to this application has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 958274.

#### Simulation of infection of a group of people during evacuation from a limited space in a panic

Anastasiia Panova1

1Bauman Moscow State Technical University, Applied Mathematics, Russia

###### Abstract

Currently, due to the increasing incidence of technological disasters and terrorist attacks on industrial and social facilities, problems arise with the rapid evacuation of people from a limited space. Due to the widespread spread of viral diseases the evacuation process, accompanied by an increased frequency of physical contacts between individuals, can lead to the spread of infection if carriers of pathogenic viruses are present in a group of people. The evacuation process is complicated by the fact that, under certain conditions panic may occur, leading to increased physical contact and a significant increase in the time people stay indoors. The evacuation time also depends on the location and shape of the obstacles located in the room. The development of mathematical models describing the dynamics of evacuation in a panic, taking into account the interaction of individuals with each other and with obstacles, provided that they are infected with a viral infection, is practically an important and urgent problem. The study of evacuation in panic conditions is possible with the help of empirical methods and methods of mathematical modeling. Physical modeling methods require significant material costs and significant human resources and provide a single empirical material that needs theoretical processing in order to clarify the basic laws of the movement of human flows during evacuation. Mathematical modeling methods are currently the most effective for developing an evacuation management strategy in a panic. Carrying out sequential calculations with subsequent statistical processing of data allows us to establish basic patterns that are tested on small experimental results. During the theoretical analysis of the results of numerical modeling recommendations can be developed for the management staff in order to increase the efficiency of evacuation. Mathematical modeling is the only means of identifying patterns of infection of people during evacuation in the case of the presence of dangerous viral diseases in the group of people. In the modern literature, there are empirical investigations that study the rate of evacuation from a limited volume through exits and corridors of various configurations. Experiments are carried out on both insects and animals, which are artificially introduced into a state of panic. A much smaller group consists of experiments on volunteers. In the course of experimental studies during evacuation from a zone with a single exit, an effect was discovered, which was called the "faster is slower" phenomenon. The meaning of this effect is the accumulation of a large number of individuals near the exit, which leads to a sharp decrease in the rate of leaving the danger zone. In our proposed model individuals are modeled by impenetrable hard round disks. Consideration of the interaction between individuals and individuals with solid obstacles is carried out by introducing an effective energy potential. The friction force is taken into account when the discs slide over the surface of obstacles and when interacting with each other. At the initial moment of time, after the announcement of the evacuation signal, the velocities of individuals are directed to the exit of the room. The modules of the initial velocity of individuals are set randomly in accordance with a uniform distribution law. The equations of motion of individuals are written in relaxation form, taking into account the source causing their movement. In panic conditions the velocity source consists of an averaged component and fluctuations distributed according to the Gauss law. If there are persons infected with dangerous viral diseases in the group, a local change in the concentration of virions near the infected is taken into account. To account for the dynamics of infection for each individual, an equation was added describing the absorption of virions by the lungs and the dynamics of the growth of the concentration of pathogens inside the infected organism. Thus, the proposed approach takes into account not only the individual behavior of each member of the group, but also the individual characteristics of the development of an infectious disease in the body. It is obvious that during the evacuation the concentration of pathogens in the body will not reach a critical level, which will lead to catastrophic consequences. However, the model allows us to simulate the further history of infection in the body of an isolated individual after evacuation from the premises. A system of stochastic ordinary differential equations describing the dynamics of both the movement of individuals and the growth of the concentration of pathogens in the body is numerically integrated on the basis of modern modified Runge–Kutta algorithms. The results of numerical simulation of evacuation of a small group of people from a room with one exit show that panic significantly increases the evacuation time. The evacuation time is determined by the difference between the exit time of the last member of the group and the time of the evacuation announcement. The influence of the shape and size of obstacles on the evacuation time is investigated. It is shown that an obstacle in the form of a square pillar significantly increases the evacuation time compared to an obstacle in the form of a round pillar. The results of modeling the evacuation time depending on the number of people in the group are presented. The dynamics of infection of a group of persons in the presence of a small number of initially infected persons is illustrated.

###### Acknowledgements:

This work was supported by the grants of Russian Foundation for Basic Research No 20-08-01061.

#### Darboux transformation and determinant representation of nonlocal complex modified Korteweg-de Vries and Maxwell–Bloch equations

Kuralay Yesmakhanova 1 , Ainur Zhumageldina2 , Zhaydary Myrzakulova3 , Anar Zhumakhanova4

1Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics, L.N. Gumilyov Eurasian National University, Department of General and Theoretical Physics, Kazakhstan
2L.N. Gumilyov Eurasian National University, Department of General and Theoretical Physics, Kazakhstan
3L.N. Gumilyov Eurasian National University, Department of Algebra and Geometry, Kazakhstan
4L.N. Gumilyov Eurasian National University, , Kazakhstan

###### Abstract

In this paper, we will focus on the (1+1)-dimensional complex modified Korteweg-de Vries and Maxwell–Bloch (cmKdV-MB) equations. Based on the idea of Muslimani and Ablowitz, we will obtain nonlocal (1+1)-dimensional cmKdV-MB equations. Darboux transformations for this equation will be constructed according to the relevant Lax pair. Its solution was obtained using the Darboux transformation. Determinant representation of Darboux transformation will be derived.

###### Acknowledgements:

This work was supported by the Ministry of Education and Science of Kazakhstan under grants AP08856912.

#### Evaluation of opportune strategies to improve knowledge in physics-a concept inventory approach

Dode Prenga1 , Megi Meta (Hysenlli) 2

1University of Tirana, Department of Physics, Albania
2University of Tirana, Departament of Physics, Albania

###### Abstract

The probability of success in physics exams is modeled herein as a logistic function of conceptual knowledge in physics and knowledge in elementary mathematics. Starting from a given level in general knowledge in physics which is recognized by a classical exam or corresponding procedural test, we set the goal to enhance it by investing somehow in the improvement of the concept inventory scores in each factor variable. We instigated by assessing abilities and difficulties for the regular-type exam in physics, and for standard CI tests in elementary calculus and conceptual physics. Next, the ability of the CI tests is improved by an amount, one computed the corresponding ability vector using logistic regression obtained in the first step, obtaining the updated estimates for each student to solve a given item of the exam and respective difficulties abilities. From them, the result of total improvement is measured directly and, the exceed of the outfit items is recorded. Now a strategy is defined as the vector of amounts of improvements of each type of CI test's abilities needed to produce a certain improvement in total ability to solve the test. The best strategy is the one that for the same amount of improvement produces a higher total ability to challenge the exam. Also, the decrease in the outfit exceed of items can be used as a qualitative or integrity estimator. This procedure is more effective if we use re-distributed scores obtained in the real exam into a few categories of didactic evaluation such as conceptualization, basic approaches, calculation, interpretation, etc. In the discussion section, we assumed that the ability to answer standard CI tests in physics is related to laboratory work or practices whereas improvement of the ability to solve CI in mathematics depends on the learning hours, therefore by that calculation we can identify what activity and in what level should we expand to achieve the desired result.

#### Multifractal and volatility analysis of multiple exchange rates.

Emiliano Alvarez1

1Universidad de la República, Quantitative Department, Faculty of Economics and Business, Uruguay

###### Abstract

In many nations, the exchange rate is crucial because it serves as a benchmark for international prices and many internal transactions, as well as a means to adjust market prices. In many countries, knowing the price of this good is essential for future transactions, so there is even a market for hedging against price fluctuations. In recent decades, analysts have examined the unpredictability of its future price and the policy options that could influence it. In numerous developing nations, macroeconomic crises have been precipitated or exacerbated by a sudden change in the exchange rate. However, it is important to inquire about the nature of the analyzed phenomenon. Are the observed price variations anomalies or are they explicable by a more general model of price formation? Is it possible to observe the effect of price contagion in countries with multiple exchange rates as well as the effect of price contagion on neighboring countries? Which prices are the most volatile, and what are their effects on the system? Is it possible to model volatility from standard constant variance models? To detect the presence of non-regular behavior, various analyses are performed on the official and unofficial daily dollar exchange rates (exchange rates) in Argentina as well as the dollar exchange rates in Brazil, Chile, and Uruguay: monofractal and multifractal analysis; multifractal spectrum; local multifractal analysis; and stochastic volatility. Inferred from these results is the presence of universal laws in the variation of these time series, as well as the absence of significant differences in the values of the parameters associated with the density of variations of the various countries, other than differences in volatility over the past few years. The combined analysis of these techniques enables us to better illustrate the various uncertainty measures associated with this important variable.

#### Wavelets in clustering time series: an application in portfolio selection using price and volume

Emiliano Alvarez1 , Juan Brida2 , Leonardo Moreno3 , Andrés Sosa4

1Universidad de la República, Quantitative Department, Faculty of Economics and Business, Uruguay
2Universidad de la República, Quantitative Methods Department, Faculty of Economics and Business, Uruguay
3Universidad de la República, Quantitative Methods Department, Faculty of Economics and Business, Uruguay
4Universidad de la República, Quantitative Methods Department, Faculty of Economics and Business, Uruguay

###### Abstract

This paper introduced a new method for clustering multidimensional time series based on wavelets that considers the time series as observations of a functional random variable. The paper generalizes previous research on stock market networks by including asset returns and volume trading as the main variables to study the financial market. The methodology is applied to examine the dynamics and structure of the Nasdaq100 stock market during the pandemic period 2019/12 - 2021/2012 considering both asset returns and volume trading to model the market. The study detects four clusters of firms corresponding with companies sharing common economic activities. The structure of the network reveals a nonlinear relationship between the variables, and the study shows that the main macroeconomic events during the period affect each cluster with different intensity.

#### Modeling a suspension for a calibrator of interferometric gravitational wave detector using finite elements method

Carlos Frajuca1

1FURG, IMEF, Brazil

###### Abstract

Interferometric gravitational wave detectors (IGWD) are very complex detectors, the need for locking the detector in a dark fringe condition besides the vibrations that affect the mirrors is very difficult challenge, creating the need for active suspension systems. These active systems make the system reach the desired sensitivity but make the calibration of such detectors much more difficult. To solve this problem a calibrator is proposed, a resonant mass gravitational wave detector could be used to detect the same signal in a narrower band and use the measured amplitude to calibrate the IGWD, as resonant mass gravitational wave detectors are easily calibrated. The main challenge in this design is the operational frequency of the calibrator, these massive detectors usually were build in frequencies close to 1 kHz but the frequencie of the Gravitaional Waves detected is around 100 Hz, then the design should adapt to this. This work aims to design and simulate a suspension of the mechanical antenna of such a calibrator. The supension is modelled in finite elements method and a design of such a suspension is presented as its normal vibration modes.

###### Acknowledgements:

CF acknowledges CNPq for grant #309098/2017-3 and #312454/2021 and FAPESP (Brazil) for grants #2013/26258-4 and #2006/56041-3.

#### Flow lines model for multiple Coulomb scattering

Vyacheslav Kurakin1 , Pavel Kurakin2

1Lebedev Physical Institute, Nuclear research, Russia
2Trapeznikov Institute of Control Sciences, , Russia

###### Abstract

Distribution function seems be the most full analytical description of any stochastic process. Distribution function for multiple Coulomb scattering for infinite and uniform medium had been obtained at the first half of the last century. We have used it successfully for the dynamics exploration of the beam crossing thin foil normally to its surface. The function mentioned cannot be used directly for the case of the foil installed at some angle to beam direction propagation. In mathematical sense, this case is already new problem and new analytical solution is required. To find out the analytical solution for this case, partial differential equation with appropriate boundary conditions must be solved. As it takes place for the majorities of the mathematical physics problems, the exact analytical solution in this specific case is unavailable. We tried to find a different approach searching for approximate solution of boundary problem based on exact solution for infinite scattering. The paper describes the flow lines model for multiple Coulomb scattering that results in analytical explanations of different phenomena taking place in the case of beam incline incidence on the border separating vacuum and scattering medium.

#### Cell migration governed by durotaxis in annual killifish epiboly

Nicolas Rojas1 , Mauricio Cerda2 , Miguel Concha3

1Universidad Catolica de Chile, IIBM, Chile

###### Abstract

The early development of annual killifish is unique among vertebrates because the group of undifferentiated embryonic cells first disperse at low density across the yolk surface during epiboly to remain in a random migratory phase before they reaggregate over a span of several days to form the embryonic axis and, consequently, the embryo proper [1-5]. In this work we propose a Maxwell model that couples the enveloping layer (EVL) stresses with cell velocities at the deep cell layer (DCL) in the first stage of epiboly. Previous theoretical results are recovered for cell speed with only a polar coordinate [6]. The numerical results of DCL velocities obtained are in good agreement with experimental data up to 30% epiboly. References [1] J. P. Wourms, “Developmental biology of annual fishes. i. stages in the normal development of austrofundulus myersi dahl,” J. Exp. Zool. 182, 143–167 (1972). [2] J. P. Wourms, “The developmental biology of annual fishes. ii. naturally occurring dispersion and reaggregation of blastomers during the development of annual fish eggs,” J. Exp. Zool. 182, 169–200 (1972). [3] J. P. Wourms, “The developmental biology of annual fishes. iii. pre-embryonic and embryonic diapause of variable duration in the eggs of annual fishes,” J. Exp. Zool. 182, 389–414 (1972). [4] G. Reig, M. Cerda, N. Sepúlveda, D. Flores, V. Castañeda, M. Tada, S. Härtel, and M. L. Concha, “Extra-embryonic tissue spreading directs early embryo morphogenesis in killifish,” Nat. Comms. 8, 15431 (2017). [5] L. Pereiro, F. Loosli, J. Fernández, S. Härtel, J. Wittbrodt, and M. Concha, “Gastrulation in an annual killifish: Molecular and cellular events during germ layer formation in austrolebia,” Dev. Dyn. 246, 812–826 (2017). [6] P. Campinho, M. Behrndt, J. Ranft, T. Risler, N. Minc, and C.-P. Heisenberg. Tension-oriented cell divisions limit anisotropic tissue tension in epithelial spreading during zebrafish epiboly. Nat. Cell Biol., 15:1405–1414 (2013).

###### Acknowledgements:

This work was funded by the National Agency for Research and Development (ANID)/PIA/ACT192015.

#### Lanczos method applications in Lattice QCD

Rudina Osmanaj1 , Klaudio Peqini2 , Dode Prenga3

1Faculty of Natural Sciences, University of Tirana, , Albania
2University of Tirana, Department of Physics, Albania
3University of Tirana, Department of Physics, Albania

###### Abstract

Numerical simulations in Lattice Quantum Chromodynamics, often have to deal with iterative solution of huge sparse linear systems of equations. Due to short recurrences or small memory requirement, Lanczos methods are some of the most proper methods for this type of problems. They can be used in different applications in LatticeQCD: numerical quadrature, matrix inversion and eigenvalues problems. In this work, we present some of the Lanczos method applications in LatticeQCD, using Boriçi Creutz fermions as chiral fermions on the lattice for simulations, implemented in FermiQCD and discuss their performance.

#### Study of SLD Model Application to Phase Behavior Calculations for Near-Critical Gas-Condensate Fluid in Tight Reservoir with Adsorption

Ilya Indrupskiy1

1Oil and Gas Research Institute of Russian Academy of Sciences, Gas, Oil, Condensate Recovery Lab, Russia

###### Abstract

Phase behavior simulations are an essential part of petroleum reservoir studies, especially for gas-condensate systems with intensive phase transitions. For conventional reservoirs, phase behavior models are based on phase equilibrium conditions in bulk. For shale reservoirs with nano-sized pores, adsorption significantly influences free fluid composition and phase behavior. Simplified Local Density (SLD) model combined with Peng-Robinson equation of state (SLD-PR) was used in a number of studies to compute fluid density and composition distributions in nano-sized pores providing pore-averaged free fluid composition. Combined with phase equilibrium conditions, it can be used for phase behavior calculations under influence of adsorption. In this study we implemented and used an SLD-based algorithm with phase behavior calculations for a real near-critical gas-condensate fluid in a tight reservoir with high pressure and temperature conditions. Though typical pore sizes for this reservoir are at least 10 times higher than in shales, adsorption was still found to be important, because even minor changes in heavier hydrocarbon concentrations led to significant changes in phase behavior due to near-critical conditions. Simulations showed that the SLD-PR model with Lennard-Jones 10-4 potential provided unphysical results for pressures of 40 MPa and higher. However, for 30 MPa the results were consistent and proved that adsorption can explain the observed difference in heavier hydrocarbons composition between fluid samples from wells and fluid extracts from cores. Phase fractions and compositions dynamics during pressure depletion were calculated for this tight reservoir and compared to bulk simulations.

###### Acknowledgements:

The study is a part of OGRI RAS research within the State Fundamental Research Program, topic 122022800272-4

#### Non-Linear Flow Simulations with Corrected Peaceman Formula for Well Pressure Calculation

Ilya Indrupskiy1

1Oil and Gas Research Institute of Russian Academy of Sciences, Gas, Oil, Condensate Recovery Lab, Russia

###### Abstract

In petroleum reservoir simulations, wells are represented by sources/sinks. Actual well pressures are not directly introduced in the numerical scheme. Instead, well pressure is related to well-block pressure (pressure in a grid block containing the well) by analytical relation called the inflow formula. To consistently match the inflow formula with numerical solution on the grid, Peaceman introduced the concept of so-called equivalent radius $R_0$ and derived the well-known formula for $R_0$ for linear (Darcy) flows. For high-velocity gas flows near wells, linear Darcy law is not valid, and non-linear two-term Forchheimer law is used instead. For Forchheimer flows, reservoir simulators use the inflow formula derived by Dake. However, the equivalent radius is still computed with Peaceman formula for linear flow. In this study, we extend the Peaceman approach to non-linear flows and derive accurate expression for equivalent radius for non-linear Forchheimer flow. This results in a correction to Dake's formula which can be neglected for large grid blocks, but becomes significant for finer grids and higher velocities. We present results of comparative flow simulations for a gas well with typical reservoir parameters and show that the effect of the introduced correction for pressure difference can be up to 11% or higher.

###### Acknowledgements:

The study is a part of OGRI RAS research within the State Fundamental Research Program, topic 122022800272-4

#### Determination of the activation energy of the reaction of decomposition ZnO gel

Challat Leila1

1Faculté des Sciences de la Technologie, Université Constantine 1, Electronique, Algeria

###### Abstract

In this work, the gel of Zinc oxide (ZnO) was prepared by sol gel method, In order to determine the activation energy of the thermal decomposition reaction of ZnO gel a theoretical approach was used . based on Thermogravimetric analysis (TGA) the curves of the loss of mass of ZnO gel according to the temperature was obtaned . the application of the isoconvertional method of FRIEDMAN for differents heating rates , 5°C/min,10°C/min, , 15°C/min, show clearly that the decomposition of gel precursor of ZnO, follows the Arrhenius law .and the value of activation energy is 92kj/mol. a physical model for kenetic of decomposition was proposed.

#### A Fractional Viscoelastic Model of the Axon in Brain White Matter

Parameshwaran Pasupathy1 , John Georgiadis2 , Assimina Pelegri3

1Rutgers, The State University of New Jersey, Department of Mechanical and Aerospace Engineering, United States
2Illinois Institute of Technology, Department of Biomedical Engineering, United States
3Rutgers, The State University of New Jersey, Department of Mechanical and Aerospace Engineering, United States

###### Abstract

Traumatic axonal injury occurs when loads experienced on the tissue-scale are transferred to the individual axons. Mechanical characterization of axon deformation especially under dynamic loads however is extremely difficult owing to their viscoelastic properties. The viscoelastic characterization of axon properties that are based on interpretation of results from in vivo brain Magnetic Resonance Elastography (MRE) and Diffusion Tensor Imaging (DTI) are dependent on the specific input frequency at which the measurements are made. In this study, we have developed a fractional viscoelastic model that characterizes the material properties of the axons and glia in the time domain. The viscoelastic powerlaw behavior observed at the tissue level is assumed to exist across scales, from the continuum macroscopic level to that of the microstructural realm of the axons. The material parameters of the axons and glia in brain white matter (BWM) are fitted to a springpot model. The 3D fractional viscoelastic model is implemented within a finite element framework. The constitutive equations defining the fractional model are coded using a vectorized user defined material (VUMAT) subroutine in ABAQUS finite element software. Using this material characterization, Representative Volume Elements (RVE) of axons embedded in glia with periodic boundary conditions are developed and subjected to time dependent loads. A homogenization scheme is created to predict the anisotropic material properties of the system as a function of its individual constituents and volume fraction of axons in glia.

#### Simulation of quantum algorithm using modified qubit rotation

Neris Sombillo1

1Ateneo de Manila University, Department of Physics, Philippines

###### Abstract

We study the implementation of Grover’s algorithm in an Ising spin chain quantum computer. In our scheme, we removed the application of time delay whenever a qubit operation is performed. Instead, we introduced a set of modified pulses that utilize the interaction of the neighboring spins. In principle, the absence of time delay pulses allows the overall rotation pulses to be applied simultaneously to execute a gate. The error arising from the unitary evolution is minimized by using soft pulses. The probability of finding the target state for both the case of unique and multiple solutions remain bounded through the application of fixed-point quantum search scheme.

###### Acknowledgements:

NI Sombillo acknowledege the Ateneo de Manila University for the travel support.

#### Restoring Coordination to Systems of Nonidentical Oscillators Through Third Party Pacing

Joseph McKinley1 , Mengsen Zhang2 , Alice Wead3 , Christine Williams4 , Emmanuelle Tognoli5 , Christopher Beetle6

1Florida Atlantic University, Department of Physics , United States
2University of North Carolina at Chapel Hill, Department of Psychiatry, United States
3Florida Atlantic University, College of Nursing, United States
4Florida Atlantic University, College of Nursing, United States
5Florida Atlantic University, Center for Complex Systems and Brain Sciences, United States
6Florida Atlantic University, Department of Physics, United States

###### Abstract

The Haken-Kelso-Bunz (HKB) model describes bistable rhythmic coordination between biological systems, capturing a wide range of empirical phenomena in brain and behavioral dynamics. The model has recently been generalized to systems of many oscillators, allowing for a quantitative study of how the dynamics of two coupled oscillators is affected by their “social environment,” i.e., by a larger system of oscillators in which both are embedded. In previous work, we studied triads of identical oscillators and showed that bistability can be restored to a monostable dyad by coupling it to a third oscillator. Here, we generalize to triads of nonidentical oscillators with different natural frequencies. We show that a pair of such oscillators, whose frequency difference would cause their dynamics in isolation to be only monostable, can exhibit bistable dynamics when both are coupled to a third oscillator having an intermediate natural frequency. We discuss some applications of this work to social and neuroscience, including gerontology and healthy aging, as well as neurostimulation and the treatment of brain-based diseases, where our findings suggest intervention strategies for promoting coordination between heterogeneous components situated in larger social environments.

###### Acknowledgements:

This work was supported by the National Institute on Aging under Grant R56-AG064094.

#### ON THE FINITE PRESENTATION OF OPERADS

My Ismail Mamouni1

1CRMEF Rabat, Mathematics, Morocco

###### Abstract

The main purpose of this paper is to prove the general result stating that if an operad O has a finite presentation, then the associate O-algebra has also a corresponding one.

#### Determination of coal calorific value using lie plant data as input parameters

lethukuthula Vilakazi1

1Tshwane University of Technology, Mechanical and Mechatronics Engineering, South Africa

###### Abstract

The gross calorific value (GCV) of coal is mainly the heat liberated to complete the combustion of coal, a higher GCV means less coal is required per unit of electricity. The CGV of coal estimates plant production costs at the time, therefore having a tool that can provide the GCV of coal by using live input plant data is paramount. The GCV of coal can be estimated by sending samples to the lab, however, there is often a delay in getting results. This paper will focus on developing a methodology that can be used to estimate the GCV of coal using live plant data as input parameters.

#### Special cases for the method of undetermined coefficients with Geogebra in non-homogeneous linear differential equations of third order

Jorge Olivares1 , Pablo Martin2 , Maria Drina Rojas3

###### Abstract

Tics and educational software have been used frequently today in these difficult times of pandemic due to COVID-19. Among the educational software, we highlight the Geogebra especially as the applets that can be built. What is intended to show in this work is to promote the various applets used in the process of teaching and learning, and in particular the solutions of linear differential equations of third order, obtained by the method of indeterminate coefficients.

#### Modeling of Thermodynamic Properties of Optical Neural Network Based on 3D Ising Model

Boris Kryzhanovsky1 , Leonid Litinskii2 , Vladislav Egorov3 , Olga Maksimova4

1Scientific Research Institute for System Analysis RAS, Center for Opto-Neuron Technologies, Russia
2Scientific Research Institute for System Analysis RAS, Center for Opto-Neuron Technologies, Russian Federation
3Cherepovets State University (CHSU), Laboratory of Mathematical and Computer Modelling of Nanostructures, Russian Federation
4Cherepovets State University (CHSU), Laboratory of Mathematical and Computer Modelling of Nanostructures, Russia

###### Abstract

We analyze a possibility to train an optical neural network by means of the Contrastive Divergence Learning method. We use a 3D Ising model with long-range interactions to investigate statistical properties of the neural network. We take into account interactions with the next-nearest and next-next-nearest neighbors and obtain analytical estimates for the critical temperature of the Ising model. Over all the interval of the interaction parameter values, our estimates are in good agreement with the results of the Monte Carlo simulations. In consistent with the current results, the heat capacity has an infinite singularity at the critical point. We show that with the growth of the number of the positive interconnections, the value of the critical temperature decreases and there are practically no restrictions for application of the Maximum-likelihood algorithm.

###### Acknowledgements:

The work is financially supported by State Program of SRISA RAS No. FNEF-2022-0003.

#### Development of engineering calculators for calculating heat flow for heating and feasibility study of building construction

Andrei Melekhin1

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

###### Abstract

The aim of the work is to create engineering calculators based on web applications using algorithms for the feasibility study of construction, thermal protection of buildings and heat flow for heating buildings. The algorithm for calculating the heat flow for heating buildings according to the enlarged parameters of the object will be based on the formula for the enlarged calculation of the heat flow, taking into account the new coefficients obtained and the new norms of specific heat energy consumption for existing and newly constructed buildings. The application of the code of rules "Thermal protection of buildings" is used as the basis of the algorithm of the feasibility study of buildings to evaluate certain building enclosing structures and determine the specific consumption of thermal energy, determine the energy efficiency class of the building in the engineering calculator. This algorithm based on this standard is designed to determine the calculated and normative specific characteristics of the consumption of thermal energy for heating and ventilation of the building, determining the class energy efficiency of the building and evaluation of the use of various options of enclosing structures during construction and reconstruction. As an economic justification for the use of types of enclosing structures , a discounted payback period for investments was applied, as well as an assessment of construction taking into account credit funds. To create an engineering calculator, the thermophysical characteristics are translated into mathematical ones. DHTML programming was used as the implementation of the calculation algorithm. The engineering calculator is implemented in a web application with the introduction of technical and economic calculation algorithms based on regulatory documentation.

#### Mathematical modelling and performance analysis of supercapacitors with variable capacitance under constant power loads

Sergio Marín-Coca1 , Stefano Bifaretti2 , Elena Roibás-Millán3 , Santiago Pindado4

1Instituto Universitario de Microgravedad "Ignacio Da Riva" (IDR/UPM), ETSI Aeronáutica y del Espacio, Universidad Politécnica de Madrid, , Spain
2Università degli Studi di Roma Tor Vergata, , Italy
3Instituto Universitario de Microgravedad "Ignacio Da Riva" (IDR/UPM), ETSI Aeronáutica y del Espacio, Universidad Politécnica de Madrid, , Spain
4Instituto Universitario de Microgravedad "Ignacio Da Riva" (IDR/UPM), ETSI Aeronáutica y del Espacio, Universidad Politécnica de Madrid, , Spain

###### Abstract

In this paper, the performance of a supercapacitor (SC) under constant power loads is studied. The equivalent electrical circuit of a SC considered in this study takes advantage of its simplicity to obtain analytical solutions. The mathematical model of the SC neglects the transient response but, due to the consideration of a variable capacitance, it accurately reproduces the steady-state response for a wide range of charging/discharging power. The integration of the governing differential equation of the SC leads to a complex relationship between SC voltage and time. From this equation several explicit expressions (i.e., charging and discharging times, ohmic losses, efficiency, etc.) as a function of the SC voltage or the state of charge (SoC) are derived. These variables are useful to size and define the energy management strategy of a SC or a bank of SCs in many constant power applications. The performance of some commercial supercapacitors that have been previously tested and modelled is analysed.

#### Lattice Boltzmann Method based model for Fluid Flow Simulations

Tejas Raval1 , Varun Sharma2 , Absar Lakdawala3

1Institute of Technology, Nirma University, Mechanical Engineering Department, India
2Nirma University, , India
3Institute of Technology, Nirma University, Mechanical Engineering Department, India

###### Abstract

Lattice Boltzmann Method (LBM) is very much popular for fluid flow applications due to its capability of implementing the physics of the problem as well as simple explicit governing equations unlike to implicit Navier- Stokes governing equations. LBM is extensively used in single and multiphase fluid flow problems. LBM based multiphase and multi component fluid flow analysis models have got wide acceptability amongst all CFD (Computational Fluid Dynamics) tools nowadays. In this paper we propose a LBM based model for Lid driven cavity problem. Main purpose behind our study is to showcase the capabilities and benefits of LB based model against well-established Navier- stokes based solvers. Benchmark problem of Lid driven cavity and 2-D channel flow are solved and numerical results are shown in the paper. Numerical results are in nice agreement with well-established experimental and conventional NS based numerical results.

###### Acknowledgements:

I sincerely thanks my mentor and Guide- Dr. A.M.Lakdawala for guiding and mentoring me for every point of time through out my journey of Ph.D and learning the topic. I also thank Nirma University, Ahmedabad, Gujarat, India for helping me directly or indirectly for conducting my research work.

#### Numerical experiments on the solution of advection equation for moving phase interface: encountered problems and their solutions

Aarne Pohjonen1

1University of Oulu, Materials and Mechanical Engineering, Finland

###### Abstract

As a part of the effort of constructing fundamentally physics based numerical model for growth of a phase in solid to solid phase transformations, a suitable mathematical description for advancing phase front and it’s numerical solution are required. The advection equation can be used for simulating of a propagating phase front. However, it is well known that simple explicit finite difference solution in this case is unstable. The Lax method provides useful numerical stabilization for the numerical scheme, but introduces numerical dissipation and broadening of the continuous function describing the diffuse phase front. Numerical experiments were made, where these problems were observed. Simple solution procedures were introduced that effectively solved the problems for time scales that were required for the numerical solver to operate in the designed context.

#### Mathematical modeling for general solution of nonlinear fractional dual-phase-lag two-temperature bioheat transfer problems

Mohamed Fahmy1

1Umm Al-Qura University, Adham University College, Saudi Arabia

###### Abstract

The main purpose of this paper is to propose a new hybrid technique which is based on the combination between fractional symmetry group improved Kudryashov method (FSGIKM) and general boundary element method (GBEM) to find the general solution of time fractional-order nonlinear dual phase lag two-temperature bioheat equation. We begin by applying the fractional symmetry group method (FSGM) based on the Riemann-Liouville fractional derivative to obtain the symmetries of this equation without dual phase lag. It is thus possible to simplify this equation into a fractional ordinary differential equation (FODE) which can be solved exactly using the improved Kudryashov method (IKM), and therefore desired conservation laws can be obtained by using Ibragimov theorem. Due to appropriateness of the GBEM for modeling of strongly nonlinear bioheat transfer problems. Subsequently, we actualized this method for modeling of the considered equation without time-fractional-order derivative. The numerical findings are depicted graphically to show the influences of nonlinearity, anisotropy and fractional-order parameter on the temperature distribution. The numerical findings also confirm the validity and accuracy of the proposed hybrid technique

#### Influence of Stratification and Bottom Boundary Layer on the Classical Ekman Model

Viviana Santander-Rodriguez1 , Manuel Diez-Minguito2 , Mayken Espinoza Andaluz3

2Andalusian Institute for Earth System Research, Dept. Structural Mechanics and Hydraulics Engineering, Spain

###### Abstract

A depth understanding of the different processes of water movements produced by the wind surface stress yields a better description and improvement of the marine food chain and ecosystem. The classical Ekman model proposes a hypothetical ocean, excluding the influence of continents, Coriolis force, an infinite depth, and assuming a constant vertical eddy viscosity. The purpose of the current study is to understand how the vertical velocity profile is affected by the variation of the eddy viscosity coefficient (Kz) and the consideration of a finite depth. The study uses an ideal analytical model with the Ekman classical model as a starting point. It has been demonstrated that, for a very stratified profile, when the depth is not considered infinity, the Ekman transport tends to angles smaller than 80o. At the same time, the classical Ekman model proposes an approximated angle equal to 90o. Considering the modified model, it was also found that the surface current deviation is smaller than 40o, which differs from the classical model's proposed, equal to 45o. In addition, it was determined that for a depth smaller than 180 m, the maximum velocity does not occur at the surface, as in the classical model, but at deeper levels.

#### Numerical modeling and simulation to study the gas hydrate dissociation in multiphase flow

Ahmed Abu-Nab1 , Alexander Koldoba2 , Elena Koldoba 3 , Yury Poveshchenko4 , Viktoriia Podryga5 , Parvin Rahimly6 , Ahmed Bakeer7

1Menoufia University, Mathematics and Computer Science, Egypt
2Moscow Institute of Physics and Technology, Dolgoprudny, Moscow, Phystech School of Applied Mathematics and Informatics, Russia
3Lomonosov Moscow State University, Department of Computational Mechanics , Russia
4Keldysh Institute of Applied Mathematics, , Russia
5Keldysh Institute of Applied Mathematics, , Russia
6Keldysh Institute of Applied Mathematics, , Russia
7Damanhur University, , Egypt

###### Abstract

The subject of studying the processes of decomposition and formation of methane hydrates (MHs) is of great importance at present, and it is a subject of research and study by many scientists around the world because of its vital role in improving the global climate, and energy sources in the future. As a result, several researchers have planned and investigated laboratory and field hydrate studies, and a simulator for methane hydrate production and dissociation in porous media has been developed. This study emphasis to describe the thermo-physical processes of MHs decomposition in porous media of a one-dimensional model in a multiphase flow. The mathematical formula of the proposed model consists of the gas, liquid and energy conservation equations, as well as the equation for the thermodynamic equilibrium between the temperature and pressure (P-T) in the hydrate stability region. The developed model was solved numerically by the technique of implicit finite differences in the network system, which can correctly describe the appearance of phase or latency as well as boundary conditions. Moreover, the systems of nonlinear algebraic equations after defining and preparing the Jacobian matrix are solved by using Newton-Raphson technique. Besides, the proposed model describes the decomposition of MHs by depressurization or thermal catalysis of the system, including the transfer of multiple temperature-dependent components in multiple stages through a porous medium. In addition, the thermodynamic effects of hydrate decomposition processes, as well as the rates of saturation of pores with water and gas during different time periods were studied.

#### Investigation of the parameters of optical radiation reflected from the multimode fiber Bragg grating

Foat Iakupov1

1Moscow Institute of Physics and Technology, Department of Photonics, Russia

###### Abstract

Fiber Bragg Gratings are an essential part of fiber lasers. Complex multimode fiber Bragg gratings (MMFBG) are used to form a resonator in multimode fiber lasers. However, it turned out that MMFBG does not only couple one transverse linearly polarized (LP) mode propagating in opposite directions, it may transfer some part of laser power from one mode into another. Since not every LP mode of active fiber has positive gain, it can lead to additional optical losses and, therefore, to laser instability and degradation. An estimation of efficiency of radiation transfer into high order transverse modes during the reflection from the MMFBG is an important problem. In this work, we developed a novel approach, which allow us to estimate this undesirable effect. Proposed theoretical model was based on coupled mode theory, and matrix approach for solving equations of modes evolution was used. Calculated elements of the reflection matrix describe interaction of LP modes propagating in opposite directions and allow to calculate all parameters of reflected radiation, such as its spectrum and modal power distribution. Reflection of every transverse mode strongly depends on its wavelength, what is defined by phase matching condition. Therefore, the reflection spectra allow us to identify modal composition of radiation and calculate relative power in every mode. We have developed this approach in this work, and now we have opportunity to restore modal composition of reflected wave. The growing interest in multimode fiber lasers and amplifiers justifies the relevance of obtained results. This data will allow to achieve higher optical power and laser stability.

#### Theoretical Study of Electronic Properties for some Environmental Contaminants: (Nitro /Anthracene)

1Alayen, Scientific Research Center; Optometry, Iraq

###### Abstract

Abstract: The electronic properties for calculating molecular structure parameters of the anthracene mixing with nitro molecules were investigated depending on the density functional theory. The best geometry for the structures of the studied molecules was investigated by using a 6-31G* basis set. The optimized structures, total energies, electronic states, energy gaps, electron affinities, global hardness, global electrophilicity, dipole moment and dipole polarizability, were calculated for the positional variation of the Nitro subgroup in the anthracene. As a result, the total energy for anthracene was increasing linearly with the change in the positions effective when added nitro molecule. Energy gap markedly reduced within change the positions effective when added nitro molecule locations first, second and ninth, where it gradually diminished, and then go up again. The forbidden energy gap was reduced and the Nitroanthracene molecule has the smallest value so the results showed a decrease in gap energies and the presence of the nitro group is likewise actively electron-withdrawing, via C−H bonds alpha to the nitro group can be acidic.

###### Acknowledgements:

We thank Al-Ayen University, for helping to complete this work.

#### Boussinesq type Equations and some Analytical Solutions

Francisco Sanchez-Bernabe1

###### Abstract

Boussinesq equations approximate the vector field velocity, pressure, and temperature of a viscous and incompressible fluid. Boussinesq equations in two dimensions are similar to Navier-Sokes equations. In fact, the first component of momentun equation of Boussinesq equations equations coincide with corresponding term of Navier-Sokes equations. However, in the second component of momentum equation of Boussinesq equations equations apperar temperature multiplied by some constants. Besides incompressibility condition, in Boussinesq equations, we have a fourth partial differential equation satisfied by temperature and both components of velocity. In this work, we consider two analytical solutions of modified time dependent Boussinesq equations. That is, there is an additional term on right hand side of the first component of momentum equation, and a source term in the energy equation satisfied by temperature. Components of velocity, pressure, and temperature of solutions presented depends on algebraic and trigonometric funcions.

#### OPTIMIZATION OF THE COVID-19 SPREADING MODEL IN A LARGE URBAN SETTLEMENT

Ilya Korshukov1

1Karaganda Medical University, Department of Informatics and Biostatistics, Kazakhstan

###### Abstract

OPTIMIZATION OF THE COVID-19 SPREADING MODEL IN A LARGE URBAN SETTLEMENT Berik Koichubekov , Aliya Takuadina , Ilya Korshukov , Marina Sorokina Department of Informatics and Biostatistics, Karaganda Medical University, 100008 Gogol st. 40, Karaganda, Kazakhstan, e-mail: info@qmu.kz, +77212503930 The COVID-19 pandemic has shown the actuality of infection spread modeling, which makes it possible to predict various scenarios for the development of the situation in the healthcare system. We have created a model based on the system dynamics methodology using the AnyLogic software. The model takes into account the demographic and epidemiological situation in a large urban settlement in Kazakhstan with a population of about 500 thousand people. However, uncertainty remains regarding such a key parameter as the Transmission rate, which is calculated as the product of ContactsPerDay * InfectionProbability. This was primarily due to the fact that throughout the pandemic, various quarantine measures have been implemented by republican and local regulatory authorities. It is difficult to assess which part of the population was under restrictions and to which extent they were followed. Therefore, to evaluate these two parameters, we used the OptQuest optimizer, included in AnyLogic. The difference between the predicted and actual number of hospitalized patients diagnosed with COVID-19 was chosen as the target function. The optimization consisted in minimizing the target function. As a result, values ContactsPerDay=13 and InfectionProbability=0.04 were obtained. Next, the accuracy of the model was evaluated using these parameter values. This research has been funded by the Ministry of Health of the Republic of Kazakhstan (Program No. BR BR11065386).

#### Rapid transition of beta barrel from arbitrary strands: A molecular dynamics observation

Saravana Prakash Thirumuruganandham1

###### Abstract

A fast molecular dynamics simulation protocol for a parallel beta barrel formation from an aribitrary tetrameric strands was discussed, using charmm-27 forcefield based NAMD molecular dynamics. In this work, we employed a tetramer unit of alanine beta strands and other amino acid mutations to investigate the folding kinetics, ionic strength, shear number, entropy, C=O--H-N bonding of barrel geometry. The results were consistent with an initial model in which oxygen placed in a rectangular like shape favours the barrel formation rather than the one with a square like oxygen topology, additionaly, we confirmed the formation of simple small barrels like geometries for different permuatations and combinations of amino acids of tetramer sub units. Also, we confirmed the stability of such barrels upon solvent exposed einvironment using 20 ns of molecular dynamics. This approach allow us to compute the barrel formation trends in neurotoxic and ion channel proteins. Our simulation supports the theoretical findings reported by Chothia and coworkers \cite{Li:8, Li:9}, and significantly well in accordance with the observation of single-walled carbon nanotube induced beta-barrel formation of the Alzheimer's Abeta 25-35 oligomers.

###### Acknowledgements:

the seed grant “Computational modeling of biomaterials and applications to bioengineering and classical and quantum machine learning for predicting social engineering (2022–2026)”, Universidad Technologica Indoamérica, Ecuador, awarded to S.P.T.

#### Thermodynamic interpretation of the open-circuit voltage for sustainable energy conversion materials

Mario Einax1

1Botswana International University of Science and Technology, Physics and Astronomy, Botswana

###### Abstract

Renewable energy converter, such as solar energy converter or thermoelectric converter, are inherently nonequilibrium systems. For example, the driving force in solar energy converter is given by the illumination. The performance of solar cell operation can be assessed by the efficiency that relates the useful output power to the total power incident. The useful output can be interpreted as the work against an applied load and the current-voltage characteristic of a solar cell represents all possible working points as function of the voltage (applied load). The discussion of fundamental limits to photovoltaic efficiencies, the enhancement of power conversion efficiencies, and efficiency forecasts has been guided the research activities in the field of renewable energy conversion. Efficiency limits can be obtained by thermodynamic arguments, for example, when looking at the zero-power operation of a solar cell or when looking at the maximum power point. The zero-power limit of a solar cell is given either under short-circuit operation, $J_{sc}(V=0)$, or under open-circuit operation. The open-circuit voltage defines a stopping point $V_{OC}$ at which the applied voltage stops the current, i.e., $J(V_{OC})=0$. Focusing on state models for bulk heterojunction organic solar cell that includes the essential optical and interfacial electronic processes, we show that the open-circuit voltage is a special thermodynamic equilibrium point, at which the state occupation probability is given by Gibbs-like distribution. The Gibbs-like distribution which can be used to calculate both the entropy $S_{ST}$ of the stopping configuration and the entropy $S_{eq}$ of the equilibrium reference state. An interesting quantitative measure of the difference between the stopping configuration and its associated “true” equilibrium configuration is given by the so-called relative entropy or Kullback-Leibler entropy (divergence) $S_{KL}$. The Thermodynamic interpretation of the open-circuit voltage provides a framework to calculate analytically the open circuit-voltage in dependence on the underlying microscopic processes. This study offers a promising route to include different types carrier recombination processes and discuss its consequence on the open-cuircuit voltage for sustainable energy conversion materials.

###### Acknowledgements:

M.E. gratefully acknowledges funding by a Research Initiation Grant at BIUST (Grant No. R00103) The financial support by the EU-AU LEAP-RE Energy Village project (Grant No. 963530) is also gratefully acknowledged.

#### A New Set of Atomic Electrohphilcity Index Values

Dimple Kumari1

1Sharda university, Chemistry, India

###### Abstract

Electronegativity is an important chemical construct which plays a major role in determining physico-chemical behaviours of atoms and molecules. There is a long list of electronegativity scales which have own advantages and limitations. Recently, we have proposed [1] two new atomic electronegativity scales based on atomic and covalent potential using Floating Spherical Gaussian Orbital (FSGO) approach. Our approach is quite simple in terms of mathematical complexity but rigorous to explain chemical properties. In this study, we have extended our work to compute atomic electrophilicity index (ω) based on our computed atomic electronegativity values. Proposed atomic electrophilicity index values nicely observe periodic trend and justify many chemical phenomena. We also have tried to establish Electrophilicity Equalization Principle (EEP) and Minimum Electrophilicity Principle (MEP) invoking our computed data. The results obtained are quite encouraging.

#### Mathematical model for to study the dynamic of COVID-19 vaccine and population behavior

MO'TASSEM AL-ARYDAH1

1khalifa university, Mathematics, United Arab Emirates

###### Abstract

We formulate a simple susceptible-vaccinated-infectious-recovery (SVIR) model to describe the spread of COVID-19. The transmission rate is decreasing function in infected and increasing in vaccinated which are the impact of caution and the sense of safety respectively. We find a formula for basic reproduction function and used it to discuss the local asymptotic stability of the disease free equilibrium (DFE). We show that the existence of the endemic equilibrium (EE) depend not only on the basic reproduction number value but also on the level of caution. We fit a modified version of the model to the cumulative number of infected in Italy, Germany, France, Spain and USA over the period from the first reported case to August 7, 2020. The model gives excellent fit to the data in these countries and the parameters values are estimated in each of these countries with 95% confidence intervals. Finally, we introduce an optimal control problem and prove that the optimal strategy of vaccination exists and is unique. The numerical simulation is used to estimate the optimal, time dependent way of introducing, vaccine under different caution levels. We show that the cost of the optimal vaccine, at all caution levels, is the lowest when compared with the costs of constant or zero vaccines.

#### Mathematical Simulation of Molecular Dynamics Processes Using the Lennard-Jones Interaction

Alexander Semenov1 , Yuriy Bebikhov2 , Mariya Semenova3 , Maxim Khazimullin 4

1Ammosov North-Eastern Federal University, Polytechnic Institute (branch) in Mirny, Russian Federation
2Ammosov North-Eastern Federal University, Polytechnic Institute (branch) in Mirny, Russia
3Ammosov North-Eastern Federal University, Polytechnic Institute (branch) in Mirny, Russia
4Institute of Molecule and Crystal Physics of UFRC RAS, , Russia

###### Abstract

The paper provides the results of mathematical simulation of molecular dynamics processes in 2D and 3D crystal structures using the Lennard-Jones potential in the MatLab software package. The theoretical part describes the differential equations for simulation, their initial and boundary conditions, and the difference approximation. The molecular dynamics simulation principle technique using one of the paired potentials was chosen. In the practical part, the chaotic motion (migration) of atoms in 2D and 3D crystal lattices has been simulated. The distribution over the computational cell and the migration of atoms beyond its limits are shown. The dependence between the bound energies in real metals and the computational model has been determined. The potential of interaction has been determined, which turns out to be positive. The amplitude-phase-frequency characteristics are obtained, which have passed the stability test.

###### Acknowledgements:

The study was supported by the Russian Science Foundation grant No. 22-22-00810, https://rscf.ru/en/project/22-22-00810/

#### Numerical analysis of turbulent forced convection in a shell and tube heat exchanger with segmental baffles

ahmed youcef1

1cder, gm, Algeria

###### Abstract

A numerical simulation of a three-dimensional turbulent flow of water in heat exchanger with six baffles and seven tubes was presented. The. The dynamic and thermal behavior of the water circulating in the shell side will be analyzed in detail using the commercial code FLUENT with the realizable k-ε model. This work contributes significantly to the understanding and control of turbulent flow. Interesting parameters of the flow have been studied, for example: the effect of mass flow variation between 0.5 kg/s and 2 kg/s, heat transfer coefficient increases by 45.19 % and 62.94 %, the pressure drop also increases from 68.82 % to about 90.82 %, the total heat transfer rate increases from 45.28 % to 64.17 %. The axial and tangential distributions of velocity and the effect of the baffles on the thermo-convective field of water in the shell are presented.

#### Numerical analysis of turbulent forced convection in a shell and tube heat exchanger with segmental baffles

ahmed youcef1

1cder, gm, Algeria

###### Abstract

A numerical simulation of a three-dimensional turbulent flow of water in heat exchanger with six baffles and seven tubes was presented. The. The dynamic and thermal behavior of the water circulating in the shell side will be analyzed in detail using the commercial code FLUENT with the realizable k-ε model. This work contributes significantly to the understanding and control of turbulent flow. Interesting parameters of the flow have been studied, for example: the effect of mass flow variation between 0.5 kg/s and 2 kg/s, heat transfer coefficient increases by 45.19 % and 62.94 %, the pressure drop also increases from 68.82 % to about 90.82 %, the total heat transfer rate increases from 45.28 % to 64.17 %. The axial and tangential distributions of velocity and the effect of the baffles on the thermo-convective field of water in the shell are presented.

#### Surface Modification Effects on Roughness of Laser Surface Textured Cylindrical Pin Joint

Solomon Ubani1

1I-Form, Dublin, Mechanical Engineering, Ireland

###### Abstract

Surface treatments are applied to materials for improving mechanical and chemical properties such as wear resistance and corrosion resistance of steel. In the industry, there is a need for improvements of the manufacturing process such as minimization of cost, high production rate and efficiency of the process. Interference fit parts typically used in the transport industry for high volume manufacture requires optimization of the assembly of components and manufacturing processes. Steel and its alloys are used mostly in manufacture but have high melting point and low viscosity due to the formation of oxides on the surface. These properties can increase the mechanical and thermal loads used in laser surface texturing of parts and can lead to fracture of the surface due to prolonged use in structures. The surface modification method before laser surface texturing and the processing parameters can reduce the compressive residual stresses and improve the performance of the pin and hub for its application. The surface texturing process can be improved by surface treatment, the depth and width of the meltpool optimized by the laser to improve the material removal rate, surface quality and life of the part used in service for interference fit joint.

#### Effects of the variation of viscosity on the stability of thin liquid film flows along a uniformly heated substrate under Heat Flux boundary condition

Dr Anandamoy Mukhopadhyay 1 , Amar Gaonkar2

1Vivekananda Mahavidyalaya, Burdwan , Mathematics , India
2IIT, Dharwad, Karnataka, Department of Mechanical, Materials and Aerospace Engineering, India

###### Abstract

It is a well known fact that the variation of thermo-physical quantities, such as, density, viscosity, surface tension, thermal diffusivity, specific heat at constant pressure etc. have substantial effects, on the dynamics and stability of the thin liquid film flows along a uniformly/non-uniformly heated substrate. The thermal boundary condition for this type of problem on the rigid heated substrate, generally considered that of specified temperature (ST) condition/ Dirichlet condition. The underlying assumption is that, the rigid substrate is thermally insulated and therefore there is no loss of heat in the solid-air interface. Although, in realistic problem, it is impossible to arrange such an insulation. Therefore, to make the problem to be more practically viable, we are interested to discuss the stability and dynamics of the thin liquid film flow along a uniformly heated substrate, where the variation of viscosity is taken care of, under heat flux (HF) boundary condition/ Newmann condition. HF boundary condition allow us to consider the heat loss in the solid-air interface. It is an experimental fact that the variation of viscosity with the moderate variation of temperature, is quite large, in comparison with other thermo-physical properties. So, all other thermo-physical quantities are assumed to be constant, just to avoid the complex mathematics involved in it.

#### Characterizing topological chaos in population models

Jose S. Canovas1

###### Abstract

We consider models of population dynamics given by difference equations. This kind of model is well-known in the literature and, in general, it is known that they can exhibit a complicated dynamical behaviour. Usually, these models are influenced by some parameters which modify the dynamics from a very simple behaviour to a complex one. For instance, we can cite [1,2,3,4]. The aim of this work is to show that the topological entropy of the model, a measure of complexity, can be a useful tool to characterize the parametric region where the dynamics are chaotic. Combining with Lyapunov exponents, we will obtain a useful characterization of observable chaos. REFERENCES: [1] R. M. May and G. F. Oster, Bifurcations and dynamic complexity in simple ecological models, Am. Nat. 110 (1976), 573-599. [2] D. J. Rodriguez, Models of growth with density regulation in more than one life stage, Theor. Popul. Biol. 34 (1988), 93-117. [3] W. E. Ricker, Stock and recruitment, J. Fisheries Res. Board Can. 11 (1954), 559-623. [4] R. J. Sacker and G. R. Sell, Almost periodicity, Ricker map, Beverton-Holt map and others, a general method, J. Difference Equ. Appl. 23 (2017), 1286-1297.

###### Acknowledgements:

This work has been supported by the grant MTM2017-84079-P funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”, by the “European Union”.

#### Approximate Solution For Second Order Fuzzy Riccati Equation.

Mazin Suhhiem1

1University of Sumer, Mathematics, Iraq

###### Abstract

In this work, we have used fuzzy homotopy analysis method to obtain the fuzzy approximate-analytical solution of the second order fuzzy Riccati equation with fuzzy initial conditions. The fuzzy series solutions that we have obtained are accurate solutions and very close to the fuzzy exact-analytical solutions. Some numerical results have been given to illustrate the efficiency of the used method.

#### MICROCONTROLLER DEVICE FOR INCREASING THE ACCURACY OF PID – REGULATORS

O Jumaev1 , G Mahmudov2 , G Rashidov3 , B Sodiqov4

1Navoi State Mining Technological University, Department of Automation and Control, Faculty of Automation, Uzbekistan
2Navoi State Mining Technological University, Department of Automation and Control, Faculty of Automation, Uzbekistan
3Tashkent State Technical University, Department of digital electronics and microelectronics, Faculty of Electronics and Automation, Uzbekistan
4Navoi State Mining Technological University, Department of Automation and Control, Faculty of Automation, Uzbekistan

###### Abstract

The article presents the developed PID controller based on a microcontroller, which allows cyclic polling of the system interface channels in real time and correction of control constants, stability and maintaining the nominal values of process parameters, where high control accuracy is required. The issues of elimination of interferences that affect the accuracy of measuring input signals in the measuring channels are considered. Methods for input and processing of signals in the form of currents and voltages in analog modules of measuring channels of the control system are presented

#### Practical Results of Experimental Studies on Purifying the Water of the Northern Territories to Drinking Quality

Yuriy Bebikhov1 , Alexander Semenov2 , Ilya Yakushev3

1Ammosov North-Eastern Federal University, Polytechnic Institute (branch) in Mirny, Russia
2Ammosov North-Eastern Federal University, Polytechnic Institute (branch) in Mirny, Russian Federation
3Ammosov North-Eastern Federal University, Polytechnic Institute (branch) in Mirny, Russia

###### Abstract

The practical application of the results of experimental studies of the aquatic environment of the Russian Federation Northern Territories has been considered for the case of the Republic of Sakha (Yakutia). Optimal water purification parameters were justified and chosen using electrocoagulation for the surface source of the Malaya Botuobiya River near the Tas-Yuryakh village. The optimal rate of water clarification and settling after electrochemical treatment is defined. The following dependencies have been obtained: water sample clarification on current density and treatment time; clarification time on power consumption; time dependence of coarse cotton settling kinetics. An accumulative-type unit with steady-state coagulation has been developed and tested for the practical application of experimental results, installed in the Tas-Yuryakh village pumping station. The following dependencies have been obtained in the research: the sludge quality on the electrolyzer current and water flow rate; the cotton settling time and quality on the electrolysis mode. The optimal water purification parameters allowed obtaining drinking quality water complying with the RF sanitary standards and regulations at the pumping station outlet. Keywords: highly colored waters, Northern Territories, electrocoagulation, water treatment, conditioning, clarification, current density, power consumption.

#### USE OF NANOPOROUS CERAMIC MEMBRANES FOR CARBON DIOXIDE CAPTURE

Idris Hashim1

1Robert Gordon University , Petroleum Engineering , United Kingdom

###### Abstract

ABSTRACT This study presents experimental results on the permeation of gases such as carbon dioxide, Air, and nitrogen through ceramic membranes with pore sizes of 200nm and 6000nm, 15nm, at temperatures of 20°C, 100°C, 150nm, and 150°C. The behaviour of gases across the membrane was depicted in the experimental results, demonstrating that pressure is a major determining factor in determining the rate of flow for gases through the membrane, as the flow rate of both co2 and air gases increased exponentially regardless of membrane geometry or operating conditions. Experimental results showed that the gas permeance for C02, Air, and Nitrogen through a ceramic membrane with different pore sizes of 15nm, 200nm, 6000nm, decreases with increasing pressure drop. It interested to note for ceramic membranes, with different pore sizes (15nm, 200nm, 6000nm) the permeance of Air is larger than that of co2. This indicated that co2 can be adsorbed by ceramic membranes. The ceramic membrane's inner surface morphology was studied. The particles are equally scattered across the ceramic membrane's surface. The ceramic membrane's surface is crack-free and smooth. contact angle measurements were also used for ceramic membrane characterization. The ceramic membrane's water contact angle is 43.54 degrees, indicating that it has a hydrophilic surface. This is due to the presence of hydroxyl (OH–) groups having hydrophilic properties on their surface and pores.

Andrey Dmitriev1 , Andrey Lebedev2 , Nadezda Abbas3 , Victor Dmitriev4 , Vasily Kornilov5

1National Research University Higher School of Economics, School of Applied Mathematics, Russian Federation
2National Research University Higher School of Economics, Laboratory of Complex Systems Modeling and Control, Russian Federation
4National Research University Higher School of Economics, Laboratory of Complex Systems Modeling and Control, Russia
5National Research University Higher School of Economics, School Business Informatics, Russian Federation

###### Abstract

The research results devoted to the construction and analysis of the stochastic nonlinear dynamic system of equations that simulate the self- organization of Twitter into the critical state are presented. A nonlinear dynamic system links three dynamic variables. The first variable corresponds to the order parameter determined by the average size of avalanches of microposts (tweets, retweets). The second variable is the conjugate field to the sizes of micropost avalanches is Tsallis entropy. The third variable is the control parameter determined by the generalized velocity of micropost distribution. Fluctuations of synergistic parameters considered in the form of additive white noise. The three-parameter scheme of selforganization allows to describe the basic properties of both a second-order phase transition and selforganization into a critical state. To describe a phase transition of the second order in a social network, the standard system of Lorenz equations in the adiabatic approximation is sufficient. To describe the transit of a social network into the self-organized criticality state, it is necessary to weaken the feedbacks by raising the order parameter (the size of the avalanches of microposts) to a fractional power and consider the fluctuations of the control parameter (the speed of microposts distribution in the network).

###### Acknowledgements:

The work is an output of a research project implemented as part of the Basic Research Program at the National Research University Higher School of Economics (HSE University).

#### Numerical simulation of water jet impact on molten material layer

Sergey Yakush1 , Nikita Sivakov2

1Ishlinsky Institute for Problems in Mechanics RAS, Laboratory of Thermal Gas Dynamics and Combustion, Russian Federation
2Ishlinsky Institute for Problems in Mechanics RAS, , Russia

###### Abstract

High-temperature melt spreading under a shallow water layer can lead to energetic interaction, known as the stratified steam explosion. One of the key uncertainties in the current understanding of this phenomenon is the mechanism for the formation of a premixed zone above the melt layer. It is known that the most energetic steam explosions occur when dispersed melt droplets are mixed with water in a certain proportion. There exists experimental evidence that high-temperature melt spreading is featured by intensive disturbances of the melt surface, visible as sporadic splashes to the height of about few centimeters. In this work, numerical simulations are performed on the interaction of a melt pool with water jets impinging on the free melt surface. Three phases are considered: melt, water, and vapor; the interfaces are modeled by the Volume of Fluid (VOF) method. Phase change is taken into account on the water-vapor interface. The problem is solved numerically in two- and three-dimensional framework. Firstly, impingement of a short-duration vertical water jet on the melt surface is studied, with the parametric analysis performed to establish the effect of the jet characteristics (mass, velocity, diameter) on the primary (due to development of a cavity on the melt surface) and secondary (central jet due to cavity collapse) splashes. Secondly, three-dimensional simulations are presented demonstrating the development of vapor film instability in an initially three-layered configuration (melt and water layers separated by a thin vapor film). Implication for the steam explosion problem is discussed.

###### Acknowledgements:

This research was funded by Russian Science Foundation (RSF) under Grant 18-19-00289

#### Conceptual Correction In Dealing With Negative Numbers & Circles

Rohit Kumar Kumar1 , Maheshwar Roy2

1Not Affiliated To Any, Physics, India
2MLS University, Udaipur, Dept. of Physics, , India

###### Abstract

It is well known fact that ‘addition is simplified using multiplication’. But do we consider this for all cases in our numerical calculations? On overlaying the data over quadrant \ number line and analyzing, it is found true, only to specific conditions. Moreover, the origin of circle and its attributes, which is in the foundation of mathematical and physical calculation is never properly understood. This improper understanding would have catastrophic impact in analyzing the results, especially at atomic or subatomic scale. Here detailed discussion regarding its origin and geometry has been done. Based on geometry, a suitable equation $$\sin(\theta/2)* \cos (\theta / 2) * 360/(\theta) , 0< \theta < 0.1$$ is derived showing the previously unknown possibilities in outcome \ calculations.

###### Acknowledgements:

Thanks to Lord Shiva for all the guidance given.

Valeriy Makarov1 , Nikita Boos2

1MIREA - Russian Technological University, Department of Bio-Cybernetic Systems and Technologies, Russian Federation
2MIREA - Russian Technological University, Department of Bio-Cybernetic Systems and Technologies, Russia

###### Abstract

The most significant difficulty with radiofrequency ablation (RFA) is insufficient heating. This problem led equipment developers to the idea of introducing cluster systems of three electrodes. Such systems have expanded the functionality of the method but still, have some limitations. To eliminate the disadvantages of the RFA method, electrode systems with an increased number of electrodes were used. The studies were carried out at the METATOM-3 radiofrequency complex. The number of electrodes was varied from 4 to 8, and the bipolar operating mode was used. The potato tuber was used as a biotissue simulator. The choice of potatoes as a simulator was associated with the peculiarities of its physical and chemical properties. Heating was carried out from the periphery of the putative tumor to the center. Various electrode systems have been developed with a number of electrodes ranging from 4 to 8. The proposed systems can be used for percutaneous, laparoscopic, or open access. The results of heating on a simulated human tissue are demonstrated. The maximum observed heating diameter was 4-5 cm, with a heating time of 10 minutes. As a result of the tests, it was found that with an increase in the number of electrodes and a transition to the bipolar mode, a significant increase in the volume of heating is possible, without increasing the procedure time, due to complete or partial refusal of switching. Heating from the periphery to the center under real conditions will reduce the risk of metastasis.

#### General static optimization of obscure numbers

Holida Primova1

1Samarkand Branch of Tashkent University of Information Technologies named after Muhammad al-Khwarizmi, Information technology, Uzbekistan

###### Abstract

This article proposes a solution to the problem of optimization based on the relation function given in the form of a triangle in an uncertain environment. In this case, the practical problem will be solved by minimizing the number and time of letters received by organizations. A statistical method has been proposed for a new approach to solving the problem of poor security. In this case, the process of adjusting the parameters by means of obscure functions was proposed. This paper also calculates the integral value of the weighted average h-level based on the triangular correlation function. And we use a statistical interpretation of the electronic document exchange system based on the theory of obscure sets. Here the triangular relation function is used.

#### Quantum gravity corrections on electron-proton and photon-proton scattering processes in quantum electrodynamics

Fidele Twagirayezu1

1University of California, Los Angeles, Physics and Astronomy, United States

###### Abstract

In this article, we study the effect of quantum gravity corrections on quantum electrodynamics (QED) scattering processes. We consider the electron-proton scattering process and, starting from modified equations of motion for both gauge and fermion fields, propagators and fermion vertex contributions with quantum corrections are obtained from the modified Lagrangian density. Scattering amplitudes and cross sections with quantum gravity corrections are obtained using modified propagators and modified currents. We deduce the modified QED Feynman rules from matrix elements and scattering amplitudes of electron-proton scattering. To learn about the veracity of the new QED rules for fermions, we apply them for photon-proton scattering. It is found that all usual expressions are recovered as the deformation parameter tends to zero. Under the assumption that the minimal length is close to the Planck scale, the result for the high-energy limit for photon-proton scattering shows a significant enhancement in the total cross-section.

###### Acknowledgements:

F.T. acknowledges the Eugene Cota-Robles Fellowship. Also, F.T. would like to thank the UCLA graduate division.

#### Statistical study of Collatz function suggests that the function picks its iterates at random

Kamal Barghout1 , Wadii Hajji2 , Nidal Abulibdeh3

1Prince Mohammad Bin Fahd University, Math and Science, Saudi Arabia
2University of Ottawa, Department of Mathematics and Statistics, Canada
3Prince Mohammad Bin Fahd University, Math & Science, Saudi Arabia

###### Abstract

A Collatz system can be represented by a physical system as it behaves similar to a system operating under a feedback design using sliding control mode. Such dynamic systems may present a statistical space that can be studied rigorously. In a previous study, the author, Barghout, presented Collatz space in a unique dynamic numerical mode by tabulating a sequential correlation pattern of division by 2 of Collatz function’s even numbers until the numbers became odd with consecutive occurrence, following an attribute of a 50:50 probability of division by 2 once as opposed to division by 2 more than once until the number became odd. The tabulated data indicated that division by 2 once process increased the starting odd number of the function while division by 2 more than once decreased it, allowing a quantification process of the direction the Collatz function’s process takes. The tabulated data also indicated that any row of data seems to extend indefinitely holding the same numerical value while any column of data repeats the same numerical subspace. This unique representation of such dynamical systems may aid in numerical analysis in mathematics and computer science. In this paper, the authors conducted a statistical study of the path of the Collatz function by studying its probabilistic contracting behavior for all positive starting odd numbers up to 1002097149, until the function leads to the first odd number that is less than the starting odd number. We present a strong indication that the function’s dynamic behavior maybe probabilistic in nature.

#### On the question of the verification of the MCNP6.2 simulation program for the NaI(Tl) detector

Rabee Alkhayat1

1University of Mosul , Physics, Iraq

###### Abstract

In this research, the Monte Carlo simulation software MCNP6.2 was used to create an extremely precise mathematical model of the 2.5 x 3.8 cm NaI(Tl) detector. The NaI(Tl) detector’s energy resolution curve and photon detection efficiency were measured using a gamma energy range of 53 to 1408 keV with various radioactive sources. Experimental efficiency values and simulation results for MCNP were consistent. However, experimental and simulated data for low photon energy revealed a discrepancy in terms of efficiency. This would be indicated by the internal attenuation of low photon energies. This work demonstrated that the MCNP6.2 software can be effectively employed to compute the energy resolution and FWHM of a 2.5 x 3.8 cm cylindrical NaI(Tl) detector. Simulation models provide precise initial calculations for the design of each detector or scientific research equipment. The energy deposition and electron track curves indicate that the employed NaI(Tl) detector was adequately sized to detect all gamma energies emitted from the radioactive sources.

###### Acknowledgements:

Thanks to Dr. Steven Federman of the University of Toledo /USA for his insightful comments.

#### An Approach to Determine the Current Distribution over Fractal Dipole Antenna

Gizem Kalender1 , Emine Zoral2 , Serkan Günel3

1Dokuz Eylül University, Electrical - Electronics Enginnering, Turkey
2Dokuz Eylül University, Electrical - Electronics Enginnering, Turkey
3Dokuz Eylül University, Electrical - Electronics Enginnering, Turkey

###### Abstract

This study presents an approach for determining current distribution over a fractal dipole antenna. In order to obtain the desired radiation pattern, the integral equations giving the current distribution of the flat dipole antenna have been examined as a first attempt. The Pocklington’s integral equation is used for determining the electromagnetic radiation from the dipole antenna [1]. The Pocklington's integral equations are in general ill-posed. Nevertheless, efficient methods have been formulated for the solution of such integral equations. Here, we consider the unknown function of the current distribution as a polynomial of finite order. The coefficients of the polynomial are obtained by optimization over the stationary point of the Iterated Function System (IFS) that yields a classical dipole antenna. $\\$ The antenna geometry is constructed as the attractor of the IFS with Random Iteration Algorithm [2]. The corresponding integral equation that gives the relationship between the current distribution over the points forming the antenna geometry and the electric field has been evaluated by using Elton’s Theorem [2]. The resulting current distribution is compared with the solution obtained by direct numerical evaluation. $\\$ Let's consider the thin wire of length $l$, which is perfectly conducting, is aligned along with the z-axis, and let $I_z(z')$ be able induced current on the surface. When the observation point is moved to the surface where $a$ is the radius, the total tangential electric field vanishes [1]. For observations on the surface, the tangential component of the electric fields can be expressed as $$E^i(z) = \frac{1}{- j \omega \epsilon}\int_{-l/2}^{l/2} I_z(z') \left[(k^2 + \frac{d^2}{dz^2})\frac{e^{-jkR}}{4 \pi R}\right]dz'$$ where $$R = \sqrt{a^2 + (z-z')^2}.$$ which is referred to as Pocklington’s integral equation [1] and can be used to determine the corresponding current density for given the incident field on the surface of the wire. The current function will be considered as a polynomial; $$I(z') = \sum_{k=0}^{N} c_k z'^k$$ where $c_k \in \mathtt{R}, k=0,1,2,...,N$ are unknown. Let us define the desired electric field $E_d$ and scattered electric field due to the current $E_s(c_k,z)$. In order to obtain $c_k$, the optimization problem is considered; $$\qquad \quad \min_{c_k} \quad \frac{1}{2}||E_d(z) - E_s(c_k,z)||^2$$ $$\text{subject to boundary conditions.}$$ To solve the optimization problem, the corresponding integral equation can be evaluated with Elton's theorem. Let $(\textbf{X},d)$ be a compact metric space. Let $\left\lbrace \textbf{X};w_{1},w_{2},...,w_{N};p_{1}, p_{2}, ..., p_{N} \right\rbrace \nonumber$ be a hyperbolic IFS with probabilities where $w_i : \textbf{X} \rightarrow \textbf{X}$ are affine maps and $p_i$ are associated probabilities. Let $\left\lbrace x_{n}\right\rbrace _{n=0}^{\infty}$ denote an orbit of the IFS produced by the Random Iteration Algorithm, starting at $x_{0}$. That is $x_{n} = \omega_{\sigma_{n}} \circ \omega_{\sigma_{n-1}} \circ ... \circ \omega_{\sigma_{1}}(x_{0})$ where the maps are chosen independently according to the probabilities $p_{1},p_{2},...p_{N}$ where $n = 1,2,...N$. Let $\mu$ be the unique invariant measure for the IFS. Then, $$\int_{\textbf{X}}f(x)d\mu(x) = \lim_{n\rightarrow \infty} \frac{1}{n+1} \sum_{k=0}^{n}f(x_{k})$$ for all continuous functions $f: \textbf{X} \rightarrow R$ and all $x_0$ [2]. Here we set $w_i$'s to yield the dipole antenna as $\textbf{X}$ geometrically using the above equation. $\\$ The current obtained as a result of the optimization problem, which is solved by calculating integrals, is compared with the current obtained by Moment Methods. The desired electric field is written by chosen as the well-known sinusoidal current approximation of the dipole. By applying partial integration, the integrals related with $m$th power of the polynomial current function can be computed directly as $$I_m = \int z^m e^{jkcos(\theta)z} dz = \frac{z^m e^{jkcos\theta z}}{jkcos\theta} - \frac{m}{jkcos\theta} I_{m-1} = z^m I_0 + \frac{m}{jk \cos \theta}I_{m-1}$$ where $$I_0 = \int z^0 e^{jkcos(\theta)z} dz = \frac{e^{-jkcos\theta z}}{-jk cos \theta}.$$ We can write this integral in a more convenient form as $$I_m = I_0 \sum_{i=0}^{m} \frac{m!}{(jk \cos \theta)^{m-i} i!} z^i$$ The results are compared and a compatible sinusoidal current distribution is obtained for the dipole antenna, which yields the other antenna parameters such as radiation patterns. Although we studied the dipole antenna as a first attempt, we consider that the results can be generalized to other fractal surfaces eventually. $\\$ $\textbf{References}$ $\\$ [1] Balanis, C. A. (2015). Antenna Theory: Analysis and Design. John Wiley and sons.$\\$ [2] Barnsley M.F. (1988). Fractal Everywhere, Academic Press, New York.

###### Acknowledgements:

This study is supported by Dokuz Eylül University, under the Department of Scientific Research Projects with project 2186.

#### Numerical investigation of the population distribution in heterogenous domain

Youwen Wang1 , Maria Vasilyeva2 , Alexey Sadovski3

1Texas A&M University - Corpus Christi, Department of Mathematics & Statistics, United States
2Texas A&M University - Corpus Christi, , United States
3Texas A&M University - Corpus Christi, Department of Mathematics & Statistics, United States

###### Abstract

We consider spatial-temporal models of population distribution in heterogeneous domain. Mathematical models of such problems are described by a nonlinear diffusion-reaction equation. We consider the problem in a two-dimensional domain with circle inclusions. To solve the problem numerically, we construct an unstructured grid that resolves inclusions on the grid level and constructs a semi-discrete system using a finite element method. For time approximation we apply a semi-implicit scheme where the reaction term of the equation is taken from the previous time layer. We present numerical results for some test problems to investigate the influence of the parameters on the time to reach equilibrium and the final equilibrium state.

#### Prediction of the survival status for multispecies competition system

Stephen Henry1 , Maria Vasilyeva2 , Alexey Sadovski3

1Texas A&M University - Corpus Christi, Department of Mathematics & Statistics, United States
2Texas A&M University - Corpus Christi, , United States
3Texas A&M University - Corpus Christi, Department of Mathematics & Statistics, United States

###### Abstract

We consider a multispecies competition model in a two-dimensional formulation. To solve the problem numerically, we construct a discrete system using finite volume approximation by space with semi-implicit time approximation. The solution of the multispecies competition model converges to the final equilibrium state that doesn't depend on the initial condition of the system. The final equilibrium state characterizes the survival status of the multispecies system (one or more species survive or no one survives). In real-world problems values of the parameters are unknown and vary in some range. For such problems, the series of Monte Carlo simulations can be used to estimate the system, where a large number of simulations is needed to be performed with random values of the parameters. A numerical solution is expensive, especially for high-dimensional problems, and requires a large amount of time to perform. In this work to reduce the cost of simulations, we use a deep neural network for fast fast prediction of the survival status. Numerical results are presented for different neural network configurations. The comparison with convenient classifiers is presented.

#### A way of contextualizing problems of eigenvalues and eigenvector in a Linear Algebra frame, using basic applications of Quantum Mechanics

###### Abstract

In the literature there are several studies that show that the mathematics teaching has been successful using contextualized problems in several areas of the physics. On the other hand, in the linear algebra texts, there are few contextualized problems in physics related with the eigenvalues and eigenvectors. So, motivated by these two latter ideas, and, in order to increase the applications to these topics in the literature, in this work we provide a way of contextualizing problems of eigenvalues and eigenvectors by using some basic applications of Quantum Mechanics. This propose is oriented for linear algebra texts. Furthermore, this proposed is designed without need of to use hard concepts of Quantum Mechanics.

#### SARS-COV-2 detection in MALDI-TOF mass spectra by machine learning

1Karaganda Medical University, Research Centre, Kazakhstan

###### Abstract

Kadyrova I.1, Kolesnichenko S.1, Kolesnikova Ye.1, Korshukov I.1, Barkhanskaya V.1, Sultanbekova A.1, Babenko D. 1 1 Research Center, Karaganda Medical University, 100000 Gogol str., 40, Karaganda, Kazakhstan, e-mail: info@qmu.kz, +77212503930 Corresponding author: Irina Kadyrova, Research Center, Karaganda Medical University, 100000 Gogol str., 40, Karaganda, Kazakhstan, e-mail: Ikadyrova@qmu.kz, tel. +7 701 503 3730 Background: COVID-19 became a travail for humanity and, especially, for the healthcare system. The pandemic revealed many gaps in the organization of medical and diagnostic processes and it led to the collapse of the inpatient and laboratory services during periods of the highest incidence. Here, we present the express method for detecting the SARS-CoV-2 virus in nasal swabs using a combination of MALDI-MS and a machine learning approach. Methods: Nasopharyngeal swabs were collected for SARS-CoV-2 RT-qPCR and MALDI-TOF MS testing from COVID-19 positive (n=203) and negative (n=101) subjects. Obtained MALDI spectra were preprocessed according to the conventional workflow including quality control, transformation, and smoothing, baseline correction, intensity calibration, etc. PCA as a dimensionality reduction technique was performed following four machine learning methods (GLM, CART, RF and XGBoost) trained and tested on preprocessed peak matrix. Results: Machine learning models RF, CART and XGBoost demonstrated the best results in the ability to distinct SARS-CoV-2 positive/negative samples with an accuracy of 100%, sensitivity of 100%, and specificity of 100%, while the GLM model achieved 71.4 % F-score and 88.8% in accuracy on the tested dataset. Conclusions: The proposed method for detecting SARS-CoV-2 in the material obtained from a nasal swab using MALDI-TOF MS and the machine learning analysis is an accessible, low time-consuming and high throughput test. The absence of the preliminary preparation of biomaterial samples and the usage of expensive reagents qualify this technique as a screening method. This research has been funded by the Ministry of Education and Science of the Republic of Kazakhstan (AP09259123)

#### Group classification and soliton solutions of coupled nonlinear Klein-Gordon equations.

Jean-Claude Ndogmo1

1University of Venda, Mathematical and Computational Sciences, South Africa

###### Abstract

We consider a system of coupled Klein-Gordon equations emanating from field theory, and perform an exhaustive symmetry classification of the nonlinear system. For the model equation associated with Higgs field, soliton and other types of solutions are found. The boundedness of some of the solutions thus found is also investigated.

#### Apparent exponential decay characteristics of dynamic and static pressure fluctuations in the multiscale-generated turbulence on the center line

Hiroki Suzuki1

1Okayama University, Graduate School of Natural Science and Technology, Japan

###### Abstract

This study presents the characteristics of pressure-related fluctuations of decaying turbulence generated by a multi-scale turbulence grid on the center line. Here, as the characteristics of pressure-related fluctuations, this study focuses on the turbulent kinetic energy related to dynamic pressure and the static pressure fluctuation RMS related to static pressure. A fractal turbulence grid used in previous studies is used as a multi-scale turbulence grid. Two turbulence grids are used in the computational conditions. In the previous study, the velocity fluctuations of multi-scale grid turbulence were pointed out to follow an apparent exponential function on the center line. This study mainly examines the characteristics of the static pressure fluctuation on the central axis. The relative static pressure fluctuation intensity, often calculated in previous studies, is also investigated. The present study approaches this issue using direct numerical analysis. The governing equations are discretized based on high-order accurate spatial discretization schemes, and the external force term reproduces the no-slip condition on the surface of the turbulence grid. In addition to the turbulent kinetic energy, this study shows that the static pressure fluctuation RMS also follows an apparent exponential function on the central axis.

#### COMPARISON OF FORECAST PERFORMANCE OF SEVERE ACUTE RESPIRATORY INFECTION INCIDENTS USING ARIMA AND TBATS MODELS IN PRE-PANDEMIC AND COVID-19 PANDEMIC PERIOD

Ilya Korshukov1

1Karaganda Medical University, Department of Informatics and Biostatistics, Kazakhstan

###### Abstract

Marina Sorokina 1, Ilya Korshukov1 , Berik Koichubekov 1, Aliya Takuadina 1 1 Department of Informatics and Biostatistics, Karaganda Medical University, 100008 Gogol st. 40, Karaganda, Kazakhstan, e-mail: info@qmu.kz, +77212503930 Corresponding author: Ilya Korshukov, Department of Informatics and Biostatistics, Karaganda Medical University, 100000 Gogol st. 40, Karaganda, Kazakhstan, e-mail: Korshukov@qmu.kz, tel. +7 771 272 48 36 Some countries including Kazakhstan conduct surveillance for hospitalised cases presenting with a severe acute respiratory infection (SARI). The prediction of new SARI cases is one of the steps taken by the competent structures of the health system in the development of measures to control and manage the non-proliferation of various viral diseases. Considering that the COVID-19 pandemic had a direct impact on the number of SARI, in this research, based on time series analysis, an attempt was made to build and compare different SARI time series forecasting models. Baseline data for SARI cases in Kazakhstan was taken from the European Center for Disease Prevention and Control (ECDC). Forecasts for one and two years were obtained from time series forecasting models ARIMA and TBATS. Models were built on the three training sets, all starting from October 2015, and in the first case ended far from the COVID-19 pandemic period, in the second case ended in the pre-pandemic period, in the third case – included one year of pandemic. The 1st period was from October 2015 to October 2018, and forecasts were for the next one (2019) and two (2019-2020) years. The following models were obtained: ARIMA(1,0,0)(0,1,0)[12] with coefficients: ar1=0.878; s.e. =0.078 and accuracy according to MAPE=28.27 and MAPE=48.35 for 2019 year and (2019-2020) years of prediction respectively. TBATS(1, {0,0}, -, {<12,5>}) with next parameters: Alpha =1.076; Gamma-1 Values=0.009; Gamma-2 Values =0.010 and MAPE=37.56 and MAPE=44.17 for 2019 year and (2019-2020) years of prediction respectively. The 2nd period was from October 2015 to February 2020, with forecasts were for the next one (2021) and two (2021-2022) years. The models were obtained: ARIMA(1,0,0)(0,1,0)[12] with coefficients: ar1=0.849; s.e.=0.076 and accuracy according to MAPE=165.0 and MAPE=101.9 for 2021 year and (2021-2022) years of prediction respectively. TBATS(1, {0,0}, -, {<12,5>}) with next parameters: Alpha =0.839; Gamma-1 Values=-0.005; Gamma-2 Values =0.012 and MAPE=86.11 and MAPE=60.12 for 2021 year and (2021-2022) years of prediction respectively. The 3rd period was from October 2015 to March 2021 and a forecast was for the next 13 months. The models were obtained: ARIMA(0,1,0)(1,1,0)[12] with coefficients: sar1=-0.278; s.e.=0.170 and accuracy for 13 months prediction: MAPE=53.73. TBATS(1, {0,0}, -, {<12,5>}) with next parameters: Alpha =0.995; Gamma-1 Values=-0.011; Gamma-2 Values =0.009 and accuracy for 13 months prediction: MAPE=44.39. The following regularities were identified in this research: the TBATS time series forecasting models compared to ARIMA models showed greater accuracy in the most cases of forecasts. SARI prediction accuracy for both created models was worst when the pre-COVID period was taken as the training set, and the forecast was already made for the period with the current COVID-19 pandemic. This research has been funded by the Ministry of Health of the Republic of Kazakhstan (Program No. BR11065386)

#### Rotating an image with a triad of non-parallel ideal lenses

Jakub Bělín1

1CEITEC BUT, Institute of Physical Engineering, Czech Republic

###### Abstract

We propose a novel imaging device, comprising three non-parallel ideal lenses. The mapping between object and image space due to this device corresponds to a rotation of the object space around a common intersection line of all included lenses. The rotation angle of the image can be set arbitrarily within a range 0 - 360° by tuning the parameters of the lenses. Our proposed device, which have called the skew-lens image rotator, could form the basis of novel applications, e.g. simulating curved spaces.

#### Planar motion of a five-link biped robot over a stepped surface with obstacles of different heights and lengths

Dmitry Fetisov1 , Dmitry Kasiyanchuk2

1Bauman Moscow State Technical University, Mathematical Modeling, Russian Federation
2Bauman Moscow State Technical University, Mathematical Modeling , Russian Federation

###### Abstract

The problem of modeling the motion of biped robots is an actual and complex problem of modern control theory. In the present paper, we deal with a special case when a five-link biped robot with knees moves along a given stepped surface. We describe the robot motion by a hybrid system which consists of a system of ordinary differential equations at the single support phase and an algebraic relation at the double support phase. For the single support phase, we suggest a set of outputs whose equality to zero corresponds to the motion inherent in human walking. We synthesize a controller providing the finite-time output stabilization, and construct a periodic motion of the robot.

###### Acknowledgements:

The work was supported by the Russian Foundation for Basic Research (project 20-07-00279)

#### Simulated study of the impact of physical parameters describing a hypothetical human cancellous bone on the ultrasonic transmitted wave - application of Biot theory.

1Acoustics and Civil Engineering Laboratory, Khemis-Miliana university, Material science department, Algeria

###### Abstract

In this work, a simulation study of the impact of physical parameters on ultrasound waves transmitted through a hypothetical sample of human cancellous bone is proposed. The sample is considered as a biphasic porous medium saturated by a fluid. The visco-inertial exchanges between the structure and the saturating fluid are described by the Biot theory modified by the Johnson model. An analytical expression of the transmission coefficient is obtained in the frequency domain. This expression depends on three physical parameters which are the porosity, the tortuosity, and the viscous characteristic length as well as on mechanical parameters; Young's modulus and Poisson's ratio of the solid and the skeleton of the medium. The transmitted signal is calculated in the frequency domain by the product of the incident signal spectrum and the transmission coefficient. In the time domain, the transmitted wave is obtained by taking the inverse Fourier transform of the reflected frequency signal. The effect of physical parameters on the transmitted signal is studied. The results obtained are discussed and compared to those given in the literature.

###### Acknowledgements:

This work was funded by the university training research project (PRFU) under No. B00L02UN440120200001 and by the General Direction of Scientific Research and Technological Development (DGRSDT).

#### Sustainability-oriented applications of the half-derivative and of the half-integral in control system design

Luca Bruzzone1

1University of Genoa, DIME, Italy

#### ELECTRICAL AND PHOTOELECTRIC PROPERTIES OF HETEROJUNCTIONS BASED ON p CdTe – n CdS AND p CdTe – n CdSe

Равшанбек Эргашев1

1Ферганский государственный университет, Физика, Uzbekistan

###### Abstract

The paper considers the photoelectric characteristics of solar cells based on film heterojunctions p CdTe – n CdS and p CdTe – n CdSe. It has been established that the spectral region of sensitivity of solar cells with the CdTe - CdS structure has a wavelength value of 0.52 and 0.85 μm. It is shown that the separation of carriers occurs not at the interface between CdS and CdTe, but in the depth of the CdTe layer, which is equal to several micrometers from the surface, which is associated with the formation of a layer as a result of diffusion of a free cadmium atom in p-CdTe.

#### Symmetry of the Fornberg-Whitham equation

Alexander Kozlov1

1Vitebsk State Medical University, Chair of medical and biological physics, Belarus

###### Abstract

The Fornberg-Whitham third-order partial differential equation was proposed to replace the general Euler equations for water waves and as it had been found at least for short wavelengths it copes with the problem successfully. Since the very beginning some attempts were undertaken to find different kinds of solutions of this equation. The Lie group approach is used in this work to reduce the Fornberg-Whitham equation to an ordinary differential one. Invariant solutions of the latter equation are solved numerically.

#### The Enhancement of Quantum Machine Learning Models via Quantum Fourier Transform in Near-term Applications

Esteban Payares1 , Juan Carlos Martinez-Santos2

1Universidad Tecnologica de Bolivar, Research department, Colombia
2Universidad Tecnologica de Bolivar, , Colombia

###### Abstract

Quantum computers are here, and the search for applications and use of these allow us to overcome the limits that today's hardware information processing gives us is constantly going on. Quantum machine learning is one of the many emerging fields that use quantum computers to process information. In this paper, we present a method and a set of experiments where we see the potential and capacity of the Noisy intermediate-scale quantum hardware for the execution of different models having as the basis in some of them the quantum algorithm corresponding to the Quantum Fourier Transform. With this, we demonstrate the effectiveness of how this algorithm can enhance the performance of quantum computations in quantum machine learning models in near-term applications. We used the systems offered by IBM Quantum and the cross-platform Python library for quantum differentiable programming Pennylane by Xanadu Quantum Technologies Inc.

###### Acknowledgements:

We want to thank the anonymous reviewers for their comments and feedback on the ideas in this paper. This work was possible thanks to the Universidad Tecnológica de Bolivar research department.

#### General features of the time data series of Covid-19 in Albania

Astrit Denaj1 , Dode Prenga2 , Valbona Tahiri3

1University of Vlora, Physics, Albania
2University of Tirana, Department of Physics, Albania
3University of Vlora "Ismail Qemali", Departmet of Physics, Albania

###### Abstract

In this work we have studied the behavior of Covid time data series for Albania, aiming on the measurement of some specific parameters of the system. By combining stationarity features of corresponding state, the empirical mode decomposition, we have identified the period November 2020, July 2021 as suitable for measurement of the most important system parameters according to the SEIR approach. For this selected period, the latent time is estimated to be around 5.4-6 days, the time lag of the most significant influence between events is obtained around 7 days. Next the forecasting and prediction for few days have been obtained by using Neural Network modeling utilized for the near to stationary regimes. Also, an empirical log periodic function is found suitable for anticipating the regime changes or local critical development. By this last method we have identified that the severity quantity measured by the report of daily causality and the new cases, has developed a nonstable regime that reached a peak and is slowing down. Dynamical properties and analysis of local processes have been analyzed by using multifractal features of the time series. Also, we used this analysis to improve identification of the more salient regimes to effectuate a meaning full measurement of a certain quantity of the system

#### Lattice Derived by Rough set as Tool for Constructing Visual Story

Tetsuya Matsui1

1Osaka Institute of Technology, Robotics and Design, Japan

###### Abstract

The "fun" of fictions or visual contents are very difficult to quantify objectively. If the method of quantifying the fun of visual contents, it may contribute to wide field. In this paper, I suggest that lattice derived by rough set is potential tool for quantifying the fun of visual contents and constructing interesting contents. Lattice derived by rough set is lattice constructed from ambiguous interpretation. I demonstrate ambiguous interpretation is important essence of fictions or visual contents, and quantifying this demonstrate ambiguous is very useful. Also, lattice derived by rough set is hopeful tool for this aim.

#### Calculation of Deflagration Appearence in Reactive Gas Mixes Flows in Two-Dimensional Regions

Sergey Martyushov1

1Moscow Aviation Institute-National Research University, Applied mathematics and Physics, Russian Federation

###### Abstract

Characteristic feature of hydrogen-air gas mix deflagration is appearance of sudden explosion after long period of induction .In this induction period grows of radicals Н, О and ОН appears. Mass of radicals, nevertheless stay small, and one radical component transverse to the others. This explosion mechanism is branching chain reaction was introduced by N.N.Semenov. Two sets of coefficients meanings where used for system of kinetic equations: the first for slow deflagration simulation, the second for calculation on the basis of branching chain reaction theory. Numerical simulation where provided for test problems of deflagration initiation from thermal spot and propagation of deflagration front in isolated cylinder and axisymmetrical channels with obstacles for gas mixes methane -air and hydrogen-air. Numerical algorithm was developed on the basis of difference schemes of Harten of second order of accuracy for time and space and Chakravarthy - Osher one of second order of accuracy for time and third order accuracy for space. Aim of calculation providing was simulation of initial stage of deflagration appearing in flows of reacting gas mixes. For specification of flow structure of investigated problem (appearing of deflagration from initial thermal spot in closed cylinder) calculations of methane -air gas mix deflagration where provided on the basis of one-reaction mode:

#### The Cosmological Black Hole

Zacharias Roupas1

1The British University in Egypt , Faculty of Energy & Environmental Engineering, Egypt

###### Abstract

We briefly review the recently novel solution of General Relativity, called the cosmological black hole, firstly discovered in [Roupas, Eur. Phys. J. C 82, 255 (2022)]. A dark energy universe and a Schwartzschild black hole are matched on a common dual event horizon which is finitely thick due to quantum indeterminacy. The system gets stabilized by a finite tangential pressure applied on the dual horizon. The fluid entropy of the system at a Tolman temperature identified with the cosmological horizon temperature is calculated to be equal with the Bekenstein-Hawking entropy.

#### Signal processing in Gamma-Ray Spectroscopy

ilker Can CELIK1

1Harran University, Physics, Turkey

###### Abstract

The design of programming interfaces like ROOT written by CERN group in Switzerland leads the way of analyzing spectroscopy mainly in nuclear physics applications. One of the topic is a signal processing in terms of currency, voltage or frequency of a radiation hitting the detector systems. Mathematical approaches finding the fit parameters in maximum Likelihood for the normal distribution and the effect of choosing the distinct methods in fitting settings will be presented in this paper.

#### Kolmogorov-Johnson-Mehl-Avrami model fitted to early COVID-19 mainland China infection outbreak data

Aarne Pohjonen1

1University of Oulu, Materials and Mechanical Engineering, Finland

###### Abstract

In 2007 Avramov provided theoretical framework which suggests that the Kolmogorov-Johnson-Mehl-Avrami (KJMA) model, which is commonly used in materials science to describe transformation phenomena, could be used in describing infection spreading in human networks. In the current article the KJMA model is fitted to the COVID-19 mainland China infection data, which consists of 29 datasets for different regions. It was found that the model provided very good fit to the datasets. The obtained values for rate constant, Avrami exponent and the initiation time are provided for all of the cases.

#### Deep Semantic Segmentation-Based Unlabeled Positive CNN’s Loss Function for Fully Automated Hamman Finger Vein Identification

1American University of Iraq-Baghdad, College of Art and Science, Computer Science Department , Iraq

###### Abstract

In recent years, biometric authentication based on finger veins has made great development to improve authentication security, however, finger-vein extraction technologies still fall into four general categories: vessel extraction, subspace-learning-based approaches, statistical-based techniques, and local-invariant-based techniques. In this paper, a new deep learning approach for human identification/verification based on deep semantic segmentation using Positive Unlabeled (PU) loss function has been proposed. The proposed system handles two main issues of finger-vein recognition using a deep learning approach. First, the lack of the training datasets, and second the integrity of the deep learning recognition scheme by proposing a fully automate deep learning approach. The first model of this approach is based on automatically generating the training dataset that has been done by using our recent model “fully automated unsupervised learning approach for finger vein binary pattern extraction”. Second, a non-traditional deep learning model for finger vein identification/verification based Unlabeled Positive loss function is proposed to extract the binary finger vein lines and identify the tested original finger vein images based on the similarity between those patterns (finger vein lines). The experimental results show that our fully automated deep semantic segmentation is able to generate a very significant clean finger vein pattern and able to successfully identify the finger vein images that belong to the same person and ignore the other by achieving on average (94%) identification similarity scores.

#### A proxy measure for addressing infeasibility in super-efficiency data envelopment analysis

Panagiotis Zervopoulos1

1University of Sharjah, Department of Management, United Arab Emirates

###### Abstract

Purpose Super-efficiency data envelopment analysis (SE-DEA) models are expressions of traditional DEA models featuring the exclusion of the unit under evaluation from the reference set. A major deficiency of SE-DEA models is the infeasibility in determining super-efficiency scores for some efficient decision making units (DMUs) when variable returns to scale (VRS) prevail. The scope of this study is the development of an oriented SE-DEA method for addressing the infeasibility problem. Methods The new method identifies a proxy unit that has minimum deviation from the actual infeasible efficient unit and uses the scale elasticity of the latter DMU. The proxy unit is introduced in an oriented linear SE-DEA model instead of the infeasible efficient unit. Results This method addresses infeasibility for efficient units even under extreme conditions (e.g., presence of zeros in inputs or outputs). At the same time, this method’s super-efficiency scores for infeasible DMUs are lower than those obtained from counterpart SE-DEA models, preventing unneeded elimination of DMUs that may be falsely deemed outliers when SE-DEA is used for outlier detection. Conclusion Our approach holds the original orientation of the SE-DEA model and identifies an optimal virtual proxy unit replacing the original infeasible DMU in the evaluation process. The proxy is the nearest unit to the actual infeasible efficient unit and is defined using the scale elasticity of the latter DMU. We present the properties and provide evidence of the performance of the proxy SE-DEA approach using conceptual and numerical examples.

#### Two-color self-similar laser beams in active periodic structures with PT-symmetry and quadratic nonlinearity

Tatiana Lysak1 , Irina Zaharova2 , Aleksey Kalinovich3

1Lomonosov Moscow State University, , Russian Federation
2Lomonosov Moscow State University, , Russia
3Lomonosov Moscow State University , , Russia

###### Abstract

Active nonlinear periodic structures with PT symmetry are characterized by the presence of both absorption and amplification of optical radiation. Quadratic nonlinearity and Bragg reflection in such periodic structures can lead to the formations of two-color solitons. Based on four coupled nonlinear Shrodinger equations, we numerically investigate self-similar propagation of laser radiation under second harmonic generation in active periodic structures. We consider the beams with finite width in transverse direction. We study the influence of incident beam width on reflection/propagation properties of active periodic structure. In our research, we consider cases of single and double Brag resonance on fundamental and second harmonic frequency.

###### Acknowledgements:

The work was supported by of the Interdisciplinary Scientific and Educational School of Moscow State University “Photonic and Quantum Technologies: Digital Medicine”.

#### VIRTUAL PERSPECTIVE METHOD IN MATHEMATICAL MODELING TECHNOLOGIES

Alexei Myshev1

1Obninsk Institute for Nuclear Power Engineering (IATE MEPHI), Department of Intelligent and Cybernetic Systems, Russian Federation

###### Abstract

The method of virtual perspective is considered, which defines the framework of the methodology of computing technologies and mathematical modeling in conditions of closedness, limitations of the computing environment, exchange and information uncertainty. The method is based on: first, models of network processors for synthesizing images of images of the results of performing procedures and operations of computation technologies in a fuzzy environment; secondly, the principles of the implementation of the perspective mechanism for virtualization processes in algorithms and procedures of computing technologies and the active memory model; third, the theory of processes with local information interaction of objects of the computing environment. Logical schemes for constructing the results of the execution of algorithms and procedures of computing technologies are implemented in the computing environment of the Hardware and Software platforms. The information environment of computing technologies of the designated platforms is a source of algorithmically uncontrollable and unmanageable errors. In such computing systems, there is no adequate formalism and computational objects of the computing environment do not have informational binding coordinate systems. Here, one should also bear in mind the peculiarities of the difference between approximations in the sense of metrics and topology. In the first case, the metric is a characteristic of how much one computed “quantum” value of the desired computation result in the allocated time slice is close to a specific other, and in the other, the topology deals with the proximity of a good computed “quantum” value of the desired result in the allocated time slice to a combination all its unacceptable values. This is not necessarily the same as the distance to the nearest bad computed “quantum” value. The information objects of the processes of computing technologies and mathematical modeling in the virtual environment of computing systems are interacting character chains, and any mathematical object of computing technologies in the memory of the information environment of the computing system is defined and described in the form of the logical structure of such chains. The environment of interaction of objects of such processes includes the following basic attributes-mediators: a virtual algorithmic variable, interaction operators, a logical structure in the address space of the limited memory of a computing system, and others, which are components of the computing environment. From an intuitive point of view, the computing environment contains everything or almost everything related to obtaining a result: it contains variables and their actual values, and they themselves are spaced not only positionally, but also contextually. The main objects (elements) of computer processes in the implementation of computing technologies are symbolic chains (words). Then the formal representation of the word a = x1… xn defines this object as a finite sequence of symbols xi from some alphabet S = {1,2,…, r} [1]. They play a double role in the dynamics of computer processes: on the one hand, they act as basic elements of symbolic models of computational technologies, and on the other, they are a source of various errors. The mechanism of such dynamics in the information environment of computing technologies is the virtual perspective.

#### EFFECT OF MICROSTRUCTURE ON THE SIMULATION OF FRACTURE OF LOW-ALLOYED STEELS

Valery Kostin1

1PEWI, Materials science, Ukraine

###### Abstract

The paper examines the influence of the microstructural state of steel on the features of crack development, deformation and fracture parameters during the simulation of the fracture process of standard samples to determine fracture viscosity parameters. Two steels with different structural states were selected - ferritic (St3sp steel) and ferrite-pearlitic (S460М steel). With the help of the developed software, the real grain structure of steels is taken into account during modeling in COMSOL Multiphysics®. In the modeling process, the influence of the microstructure on the size of the crack opening, the speed of the crack growth, the total elastic energy of deformation, the value of J-integral and the stress intensity factor were established. The comparison of experimental and calculated results showed that in the case of low energy of the grain boundaries, the destruction occurs along the grain boundaries, while at high energy - along the body of the grains, which is in good agreement with the results of macro- and microscopic studies of the fracture surface of standard samples.

#### Contact process in habitat fragments linked by corridors

Ingrid Carolina Ibagon Pardo1 , Alexandre Furlan2 , Ronald Dickman3

1Universidade Federal de Minas Gerais, Physics, Brazil
2Universidade Federal de Minas Gerais, Physics, Brazil
3Universidade Federal de Minas Gerais, Physics , Brazil

###### Abstract

We study the effect of a corridor connecting two regions on the lifetime of species in fragmented habitats. Three Markov processes exhibiting extinction/survival phase transition are analyzed: the basic contact process (CP), the diffusive contact process, and the two-species contact process (2SCP). These contact processes are studied in square lattices. In the basic CP each lattice site can be empty or occupied by an individual, reproduction at vacant nearest neighbors(NN) occurs at rate $\lambda$ and death at rate unity. In the diffusive CP, in addition to reproduction and death, each individual attempts to hop to one of its NN sites at rate $D$. Finally, on the 2SCP each lattice site can be occupied by individuals of species A and/or B and the death rate at sites occupied by both species is $\mu<1$ ($\mu>1$) for positive(negative) interspecific interaction. We find that connecting two regions increases the lifetime when the reproduction rate is greater than its critical value. The lifetime enhancement increases with the reproduction rate; wide and short corridors provide the best enhancement. However, populations with a higher diffusion rate are less sensitive to corridor shape.

#### Modeling of post-infusion application of external pressure for uniform thickness of polymeric composite parts and increase in fiber volume fraction

Igor Zhilyaev1

1FHNW School of Engineering, Institute of Polymer Engineering, Switzerland

###### Abstract

Vacuum infusion processes in the production of polymeric composite structures have become increasingly popular in recent years due to the simplicity of their implementation and the low cost of technological equipment. However, the scope of such processes is limited to lightly loaded composite structures, which is due to the relatively small value and uneven distribution of the reinforcing fibers volume fraction, as well as a significant variation in the resulting wall thickness of finished parts. The reason for this is that at the end of the infusion stage of the process, a significant internal pressure gradient is maintained in the porous preform. In some works, a modification of the process has been proposed and experimentally substantiated, which consists in the application of controlled external pressure to the preform being vacuumed with a gradual increase in pressure in the vacuum vent to atmospheric pressure. Variations of this process include a so called preform flushing, in which excess resin is removed from the preform through inlets and outlets. It is noted that the resulting porosity of the molded part depends on the factors of time, rate and maximum value of applied pressure. For the correct choice of the process modes, its computer model based on the concept of poroelasticity was developed, which complements the previously developed multiphysical model of vacuum infusion. The state of the preform at the end of the infusion stage is the input to the model of post-infusion exposure of the preform to external pressure. This model, which implements the solution of a complicated version of the classical Mandel problem, is based on the joint use of the Darcy law, continuity, and compressibility equations for a curing liquid resin and a porous medium. The results of process simulation in the Comsol Multiphysics environment provide a reconstruction of the distribution of pressure, porosity, thickness of a thin-walled workpiece during and after the change in controlled pressures, allowing you to achieve the best achievable quality objectives for given resin and preform properties.

#### Geothermal Energy for Refrigeration and Air Conditioning, Sustainable Development, and the Environment

Abdeen Omer1

1Energy Research Institute (ERI), , United Kingdom

###### Abstract

Geothermal heat pumps (GSHPs), or direct expansion (DX) ground source heat pumps, are a highly efficient renewable energy technology, which uses the earth, groundwater or surface water as a heat source when operating in heating mode or as a heat sink when operating in a cooling mode. It is receiving increasing interest because of its potential to decrease primary energy consumption and thus reduce emissions of the greenhouse gases (GHGs). The main concept of this technology is that it uses the lower temperature of the ground (approximately &lt;32°C), which remains relatively stable throughout the year, to provide space heating, cooling and domestic hot water inside the building area. The main goal of this study was to stimulate the uptake of the GSHPs. Some emphasis has recently been put on the utilisation of the ambient energy from ground source and other renewable energy sources in order to stimulate alternative energy sources for heating and cooling of buildings. Exploitation of renewable energy sources and particularly ground heat in buildings can significantly contribute towards reducing dependency on fossil fuels. This section highlights the potential energy saving that could be achieved through use of ground energy source. This study highlights the energy problem and the possible saving that can be achieved through the use of ground sources energy. Also, this study clarifies the background of the study, highlights the potential energy saving that could be achieved through use of ground energy source and describes the objectives, approach and scope of the thesis. It also focuses on the optimisation and improvement of the operation conditions of the heat cycles and performances of the GSHP. It was recommended that GSHPs are extendable to more comprehensive applications combined with the ground heat exchanger in foundation piles and the seasonal thermal energy storage from solar thermal collectors. Therefore, an approach is needed to integrate renewable energies in a way to meet high building performance. However, because renewable energy sources are stochastic and geographically diffuse, their ability to match demand is determined either by the utili-sation of a greater capture area than that occupied by the community to be supplied or the reduction of the community’s energy demands to a level commensuratable with the locally available renewable resources.

#### Numerical approach for incompressible fluid flows in and around a pair of porous elliptic cylinders

D. Palaniappan1 , Maria Vasilyeva2

1Texas A&M University, Corpus Christi, Mathematics & Statistics, United States
2Texas A&M University - Corpus Christi, , United States

###### Abstract

In this study we consider numerical simulations of incompressible fluid flow around and through a pair of porous/permeable elliptic cylinders. The mathematical model set up is based on Navier-Stokes (NS) equations in the free fluid domain Ωf together with convective Darcy- Brinkman-Forchheimer (CDBF) equations in the porous subdomains Ωp occupied by the two cylinders with an elliptical cross section. Continuity of velocity and stress boundary conditions are assumed at the interfaces separating the two fluid phases. Finite Element method based numerical approach is employed to study the two-dimensional flow problem. Numerical simu- lations are performed for various orientations of the ellipses, or equivalently, different angles of attack of the original flow. Results for different choices of the Reynolds number Re, the Forch- heimer coefficient C, the Darcy number Da and the two eccentricity parameters e1 and e2 are computed, demonstrating the efficacy of our approach. The numerical solutions and simulations presented here are of some interest in modeling the filtration of incompressible fluids through non-circular porous inclusions.

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