## Conference submissions

#### Visualizing numerical solutions of linear second order differential equations with Euler's method and Lagrange interpolation via GeoGebra

Jorge Olivares Funes1 , Elvis Valero2

1Universidad de Antofagasta, Mathematics , Chile
2University Tarapaca, mathematics, Chile

###### Abstract

In this work, we will show the algebraic and graphic expressions, which were obtained through the Euler method and Lagrange interpolation with GeoGebra software for some Second-order linear differential equations. These applets were designed for the course of differential equations and numerical calculation for Engineering careers at the University of Antofagasta, Chile.

#### Numerical solution of Hermite differential equations using the spline method of order 1 with GeoGebra

Jorge Olivares Funes1 , Elvis Valero2

1Universidad de Antofagasta, Mathematics , Chile
2University Tarapaca, mathematics, Chile

###### Abstract

In this paper, we will show the approximations, which can be obtained, by means of the spline method of order 1, for Hermite's differential equations With very interactive examples of GeoGebra applets. The GeoGebra program today has many applications and uses, and among them, we will dedicate ourselves to making known, the great benefit that can be obtained, in the process of generating new mathematical knowledge for learning and teaching the numerical solutions of differential equations.

#### Statistical modelling of factor analysis to set causals of hybrid learning success during Covid-19 lockdown

Agustin Vazquez-Sanchez1 , Carlos Alberto Cruz Villar2 , Francisco Delgado3 , Ezequiel Chavez-Alcaraz4 , Jesus Chong-Quero5

1Tecnologico de Monterrey, Mechatronics, Mexico
2Tecnologico de Monterrey, Mechatronics, Mexico
3Tecnologico de Monterrey , Physics and Mathematics, Mexico
4Tecnologico de Monterrey, Mechatronics, Mexico
5Tecnologico de Monterrey, Mechatronics, Mexico

###### Abstract

Around the world, Covid-19 outbreak caused a sudden and forced migration from face-to-face education to online education generating an unprecedented phenomenon in the history of education. In Mexico, the most affected Education level was Basic Public Education, the least unprepared while Private Higher Education has experienced by years alternative models using technology. Despite, around the world, new findings arose evidencing that students could require emotional support under the confinement due to the extended lockdown and an intense effort to follow their new educative plans revealing behavioral issues as success factors of that extended online education in the emergent strategy. Based on a statistical model of exploratory factor analysis of data applied to Freshman and Sophomore engineering students, this work presents a roadmap of statistical modelling and testing for the analysis of several dimensions of more effective causal in the success of the forced online education paradigm implementation. Obtaining a Cronbach-alpha value of 0.817, it points to meaningful internal reliability to discriminate and rearrange those causal and dimensions into a more comprehensive education ecosystem.

###### Acknowledgements:

Authors would like to acknowledge the financial support of Novus Grant with PEP no.PHHT023-1920ZZ00023 and Writinglab, Institute of Future Education, both initiatives ofTecnologico de Monterrey, Mexico, in the development and production of this work.

#### Post-selected double teleportation and the modelling of its related non-local properties

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

###### Abstract

Quantum teleportation is a notable basement of quantum processing. It has been experimentally tested with an outstanding growing success by introducing improvements and applied advances in the last two decades. Its quantum non-local properties have let to discover and to introduce novel implementations based on it in quantum processing, cryptography, quantum resources generation among others. In the current work, we develop a scheme performing double teleportation on two different virtual receivers, while the sender is still able to post-select the final target of teleportation. In addition, we present the theoretical modelling of several interesting effects thus generated, where virtual teleported states are processed and combined to reach certain non-local effects useful in the terrains of cryptography, quantum communication, and quantum resources generation on demand. Last effects require that sender and receivers play certain cooperation roles in the process. Notable effects surpassing their classical analogues are then presented, thus showing the outstanding value of teleportation in the quantum mechanics applications. They are analysed in terms of their parametric behavior, limitations, and scalability.

###### Acknowledgements:

Authors would like to acknowledge the financial support of Novus Grant with PEP no. PHHT023-1920ZZ00018 and Writinglab, Institute of Future Education, both initiatives of Tecnologico de Monterrey, Mexico, in the development and production of this work.

#### Calculating value of π by splitting technique 2013

Fazal Rehman1

1GHSS GUMBAT KOHAT PAKISTAN, Maths, Pakistan

###### Abstract

This paper propose geometrical technique to obtain the value of π from splitting a circle in 4 Equilateral triangles 1 square and 4 sectors.It is first ever study to calculate the value of π by splitting a circle in these shapes and then by combining areas of these shapes value of π can be calculated.

#### Galarkin Method with GeoGebra in Differential Equations

Jorge Olivares Funes1 , Elvis Valero2 , Pablo Martin3

1Universidad de Antofagasta, Mathematics , Chile
2University Tarapaca, mathematics, Chile
3University Antofagasta, Physical, Chile

###### Abstract

Consider $$\frac{d^2y}{dx^2} + P(x)\ y=Q(x,a)$$ , y(0)=y(1)=0 , $$x ,a\in(0,1)$$ In the next paper, we will solve these kinds of differential equations, using Galerkin's numerical method with GeoGebra support. The differential equations that will be shown to me will be those used in various applications of science and engineering.

#### Geoexchanger System for Buildings Heating and Cooling

Abdeen Omer1

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

###### Abstract

Geothermal heat pumps (GSHPs), or direct expansion (DX) ground source heat pumps, are a highly efficient renewable energy technology, which uses the earth, groundwater or surface water as a heat source when operating in heating mode or as a heat sink when operating in a cooling mode. It is receiving increasing interest because of its potential to reduce primary energy consumption and thus reduce emissions of the greenhouse gases (GHGs). The main concept of this technology is that it utilises 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 is to stimulate the uptake of the GSHPs. Recent attempts to stimulate alternative energy sources for heating and cooling of buildings has emphasised the utilisation of the ambient energy from ground source and other renewable energy sources. The purpose of this study, however, is to examine the means of reduction of energy consumption in buildings, identify GSHPs as an environmental friendly technology able to provide efficient utilisation of energy in the buildings sector, promote using GSHPs applications as an optimum means of heating and cooling, and to present typical applications and recent advances of the DX GSHPs. The study highlighted the potential energy saving that could be achieved through the use of ground energy sources. It also focuses on the optimisation and improvement of the operation conditions of the heat cycle and performance of the DX GSHP. It is concluded that the direct expansion of the GSHP, combined with the ground heat exchanger in foundation piles and the seasonal thermal energy storage from solar thermal collectors, is extendable to more comprehensive applications.

#### The Center and the Barycenter

Volker Thürey1

1None, Bremen, Germany

###### Abstract

In the first part we deal with the question which points we have to connect to generate a nonself-intersectioning polygon. Afterwards we introduce polyholes, which is a generalization of polygons. Roughly spoken a polyhole is a big polygon, where we cut out a finite number of small polygons. In the second part we present two centers', which we call center and barycenter. In the case that both centers coincide, we call these polygons as nice. We show that if a polygon has two symmetry axes, it is nice. We yield examples of polygons with a single symmetry axis which are nice and which are not nice. In a third part we introduce the Spieker center and the Point center for polygons. We define beautiful polygons and perfect polygons. We show that all symmetry axes intersect in a single point.

#### Spontaneous Order in Organic Monolayers

Alokmay Datta1

1CSIR-Central Glass and Ceramic Research Institute, Materials Characterization and Instrumentation, India

###### Abstract

Spontaneous ordering in a monolayer of three-atom models of lipid molecules at the surface of water has been observed through Monte Carlo simulation. The monolayer is the simplest planar bio-mimic of the cell wall in contact with water. Ordering has been studied in the absence and presence of physiologically relevant cations at different cation ratios to understand the role of the Na/K ratio on cell membrane dynamics. Comparison with experimental results obtained from compression studies of the monolayers is also presented.

#### Leaf Surface Reconstruction Using A Hybrid Interpolation Finite Element Method

Moa'ath Oqielat1

1Al balqa Applied University, Mathematics, Jordan

###### Abstract

The goals of the research presented in this paper are first, construction a leaf surface from large real 3D scanned data points using a new hybrid interpolation finite element method so-called a hybrid clough-Tocher cubic polynomial interpolation method (CT-CPI). Secondly, a comparison between the hybrid CT-CPI method and hybrid CT-Taylor series method (CT-TS) for the leaf surface reconstruction is presented. Realistic leaf surfaces models are essential for many applications in the sciences of plant, such as modelling spray and spreading droplet movement on the surface, photosynthesis and a canopy light environment or it can be implemented for visual purposes only. For these goals, a precise mathematical depiction of the boundary and surface is mandatory. Although an operative method is to apply either CT-TS or CT-CPI algorithm to recreate the surface of the leaf from 3D scanned data, difficulties occur when dealing with Anthurium leaves, which tend to have many branches. To solve this issue, we implemented interpolating in combined with the CT method. Our algorithm uses finite element methods to represent the surface as a mesh of triangles. Numerical results confirm that the CT-CPI techniques produces more realistic virtual representations of Anthurium leaves than using CT-TS method.

#### Calculation of magnetic susceptibility of magnetic molecular cluster Mn12 with considering quadrupole excitations

yousef yousefi1

1Payam-e-Noor, physics, Iran, Islamic Republic Of

###### Abstract

The temperature dependence of the magnetic susceptibility of the Mn12 magnetic molecular cluster is investigated in different fields. Until now, only dipole excitations were considered in calculations to calculate magnetic susceptibility, but due to the spin number of this molecular cluster and to obtain higher computational accuracy, more multipolar excitations had to be included in the calculations. For this purpose, in this paper, in the calculations related to the magnetic susceptibility of the molecule, in addition to dipolar excitations, quadrupole excitations are also considered, and the relevant diagrams are drawn. Calculations show that the results obtained in a situation where quadrupole excitations are considered, are more consistent with the experimental results.

#### The Spherical Bessel function j0 in fractional differential equations

Jorge Olivares Funes1 , Pablo Martin2 , Elvis Valero3

1Universidad de Antofagasta, Mathematics , Chile
2University Antofagasta, Physical, Chile
3University Tarapaca, mathematics, Chile

###### Abstract

Bessel's spherical functions have had many important applications in engineering and optics and science. In this work that is a continuation of The error function in fractional differential equations, showed how to solve the fractional differential equation $$\frac{d^\alpha y}{{dx}^\alpha}= j_0(x)$$, $$y^{\left(k\right)}(0)= 0$$ ,$$k=0..m-1$$, with m=1,2,3... . Where the nonhomogenous part is the function Bessel Spherical j0 (x)

#### The effects of gravitational potential on chemical reaction rates

Paola Lecca1

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

###### Abstract

In this study we aim to answer through a mathematical model and its numerical simulation the question whether the kinetic rate constants of chemical reactions are influenced by the strength of gravitational field. In order to calculate the effects of gravity on the kinetic rate constants, we correct the mathematical model of the expression of these constants known from the collision theory of chemical kinetics, recasting it in the context of general relativity. The reformulation of the classical chemical kinetic model is based on the remodelling of (i) the Maxwell-Bolzann distribution and (ii) the collision frequency between molecules/atoms of chemical species due to time dilation. The model predicts that the relative velocity between the colliding molecules/atoms is higher at higher gravitational potential. Using numerical simulations, we quantitatively estimate the orders of magnitude by which the kinetic constants vary as a function of varying the strength of the gravitational field. In addition, we present a numerical estimation of the two effects affecting the rate constant, namely the spatial reorganisation of the particle distribution due to gravitational force and the effect of time slowing down as the intensity of the gravitational field increases.

#### Plasma sheath expansion around a defect on the cathode

1 K.N. Toosi University of Technology, Physics, Iran, Islamic Republic Of

###### Abstract

In this work, we numerically investigate the sheath dynamics of an electropositive plasma around a defect on the cathode by using the hydrodynamics equations. It is assumed that the plasma consists of electrons and singly charged positive ions. The finding of this work has a great importance in plasma ion implantation technique.

#### Development of engineering calculator to copmutation the heat flux

Andrei Melekhin1

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

###### Abstract

The author has developed an engineering calculator for calculating the heat flow for heating buildings according to the enlarged parameters of the object. The algorithm of the calculator is based on the method of determining the amount of heat energy and heat carrier in water supply systems of urban heat supply. The author carried out a systematic analysis of the heat loads on the heating of buildings in Russia according to the data of implemented construction projects. With this in mind, new coefficients a, n were calculated to determine the specific thermal characteristics of the building for newly constructed buildings. Adjusted the algorithm for calculating the heat supply of buildings according to the enlarged parameters of the object. The calculation algorithm is implemented in the software product using DHTML programming.

#### Superposition of states in parallel computing algorithms.

Tomasz Kuczerski1

1Military Institute of Armament Technology, Zielonka, Poland

###### Abstract

The paper describes a practical application of parallel computing using state superposition. Simulations are conducted in Python language using computational libraries. The author presents the possibilities of using ready-made computational libraries to implement modern algorithms based on superposition of states. As a result, the results of the algorithm implemented using parallel computing are presented. Furthermore, the possibilities of using the above algorithms to accelerate classical computations are described.

#### On the asymptotic stability of advection-diffusion equations of mass transport in bubble column bioreactor

Paola Lecca1 , Angela Re2

1Free University of Bozen-Bolzano, Faculty of Computer Science, Italy
2Fondazione Istituto Italiano di Tecnologia,, Centre for Sustainable Future Technologies, Environment Park - Parco Scientifico Tecnologico per l’Ambiente, Italy

###### Abstract

This study presents an asymptotic analysis of a model of a bioreactor converting carbon monoxide (CO) gas into ethanol through a C. autoethanogenum biocatalyst [1]. The configuration is a bubble column reactor with co-current gas-liquid flows where gas feed is introduced a gas distributor placed at the bottom of the column. A pure culture of C. autoethanogenum is subsequently injected at the bottom of the column; therein cells are dispersed in the liquids and consume the dissolved gas and release by-products such as ethanol and acetic acid. A spatial gradient establishes in the column since gas concentration decreases as gas flows up due to cellular consumption. Consequently, cellular growth and byproduct secretion are affected by spatially varying dissolved gas concentrations. The model accounts for four species representing the biomass, the CO substrate in the liquid phase, and two by-products - ethanol and acetic acid. While the equations of the ethanol and acetate dynamics are taken from Chen’s work [2], in our model the dynamics of the substrate is described by an advection-diffusion equation with no sink/source terms depending on the biomass. This allows the calculation of closed-form solution for the substrate dynamics, that is used in the calculation of the bacterial growth rate [3]. We investigate the asymptotic stability of this solution, i.e. the stability of the solution at the top of the bioreactor. The asymptotic stability property is particularly important to ensure the usability of measurements made in regions of the bioreactor away from the microorganism and nutrient input (output) point to establish controllability and/or optimal controllability of the bacterial fermentation process. The controllability of the system in turn allows the possibility of modulating the ethanol production efficiency. In the absence of asymptotic stability, the exploitation of physical mass transport processes other than free advection and diffusion is not recommended. Possible scenarios will be proposed and analysed. References [1] Norman, R.O.J, Millat T., Winzer, K., Minton,, N.P., Hodgman, C. Progress towards platform chemical production using Clostridium autoethanogenum. Biochem Soc Trans. 2018; 46(3):523-535. doi: https://doi.org/10.1042/BST20170259 [2] Chen J., Gomez,J.A., Hoeffner, K., Barton, P.I., Henson, M.A.: Metabolic modeling of synthesis gas fermentation in bubble column reactors. Biotechnol. Biofuels 8(1) (2015). https://doi.org/10.1186/s13068-015-0272-5 [3] Lecca P., Re A.: Observability of Bacterial Growth Models in Bubble Column Bioreactors. In: Cazzaniga P., Besozzi D., Merelli I., Manzoni L. (eds) Computational Intelligence Methods for Bioinformatics and Biostatistics. CIBB 2019. Lecture Notes in Computer Science, vol 12313 (2020). Springer, Cham. https://doi.org/10.1007/978-3-030-63061-4_27

#### Gamma-Variance Model: Fractional Fourier Transform (FRFT)

Aubain Nzokem1

1York University, Mathematics & Statistics, Canada

###### Abstract

The paper examines the Fractional Fourier Transform (FRFT) based technique as a tool for obtaining the probability density function and its derivatives; and broadly for fitting stochastic model with the fundamental probabilistic relationships of infinite divisibility. The probability density functions are computed and the distributional proprieties are reviewed for Variance-Gamma (VG) model. The VG model has been increasingly used as an alternative to the Classical Lognormal Model (CLM) in modeling asset prices. The VG model was estimated by the FRFT. The data comes from the SPY historical data, the SPDR S\&P 500 ETF (SPY). The Kolmogorov-Smirnov (KS) goodness-of-fit shows that the VG model fits better the cumulative distribution of the sample data than the CLM. The best VG model comes from the FRFT estimation.

#### Classes of Dynamic Systems with Various Combinations of Multipliers in Their Reciprocal Polynomial Right Parts

Irina Andreeva1

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

###### Abstract

A family of differential dynamic systems is considered on a real plane of their phase variables x, y. The main common feature of systems under consideration is: every particular system includes equations with polynomial right parts of the third order in one equation and of the second order in another one. These polynomials are mutually reciprocal, i.e. their decompositions into forms of lower orders do not contain common multipliers. The whole family of dynamic systems has been split into subfamilies according to the numbers of different reciprocal multipliers in the decompositions and depending on an order of sequence of different roots of polynomials. Every subfamily has been studied in a Poincare circle using Poincare mappings. A plan of the investigation for each selected subfamily of dynamic systems includes the following steps.  We determine a list of singular points of systems of the fixed subfamily in a Poincare circle. For every singular point in the list we use the notions of a saddle (S) and node (N) bundles of adjacent to this point semi trajectories, of a separatrix of the singular point, and of a topo-dynamical type of the singular point (its TD – type).  Further we split the family under consideration to subfamilies of different levels with proper numbers. For every chosen subfamily we reveal topo-dynamical types of singular points and separatrices of them. We investigate the separatrices’ behavior for all singular points of systems belong to the chosen subfamily. Very important are: a question of a uniqueness of a continuation of every given separatrix from a small neighborhood of a singular point to all the lengths of this separatrix, as well as a question of a mutual arrangement of all separatrices in a Poincare circle Ω. We answer these questions for all subfamilies of studied systems. The presented work is devoted to the original study. The main task of the work is to depict and describe all different in the topological meaning phase portraits in a Poincare circle, possible for the dynamical differential systems belonging to a broad family under consideration, and to its numerical subfamilies of different hierarchical levels. This is a theoretical work, but due to special research methods it may be useful for applied studies of dynamic systems with polynomial right parts. Author hopes that this work may be interesting and useful for researchers as well as for students and postgraduates.  As a result we depict phase portraits of dynamic systems of a given family and outline the criteria of every portrait appearance.

#### 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, , 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 very successfully used for development and subsequent 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, by and large, only sufficient conditions for the theoretical stability (at semi-infinite time intervals) of a number of dynamic equilibrium states with respect to both small and finite perturbations, but from 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. Summation is performed on repeating lower index $i$ throughout the report. 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 Boussinesq 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. This theorem states that any equilibrium configuration of point electric charges is unstable if, besides its own Coulomb forces of attraction and repulsion, no other forces act on them. 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.

###### Acknowledgements:

Authors would like to acknowledge the financial support of China Scholarship Council.

#### Stochastic Analysis of SIS Epidemic Model

Aubain Nzokem1

1York University, Mathematics & Statistics, Canada

###### Abstract

We are interested in describing the infected size of the SIS Epidemic model using Birth-Death Markov process. The Susceptible-Infected-Susceptible (SIS) model is defined in a constant size ($M$) population. The life span of each individual in the population is modelled by an exponential distribution with parameter $\alpha$, and the disease spreads within the population is modelled by a Poisson process with a rate $\lambda_{I}$. $\lambda_{I}=\beta I(1-\frac{I}{M})$ is similar to the instantaneous rate in the logistic population growth model. The analysis is focused on the disease outbreak, where the reproduction number $R=\frac{\beta} {\alpha}$ is greater than one. As methodology, we use both numerical and analytical approaches. The numerical approach shows the infected size dynamics through sample-path simulations and the relationship $R$. As $M$ becomes large, some stable statistical characteristics of the infected size distribution appear. And the infected size is shown analytically to follow a normal distribution with mean $(1-\frac{1}{R}) M$ and Variance $\frac{M}{R}$

###### Acknowledgements:

Julio Espinoza-Ortiz1 , Roberto Lagos-Monaco2

1 Federal University of Catalão, Physics, Brazil

###### Abstract

We consider a Bunimovich like quarter-stadium by softening the non zero y-boundary. The smoothing is performed via an exponent monomial potential, the system becomes not completely reflective but preserves the particle's translation and rotational motion. Increasing the exponent value, the stadium's boundaries become rigid and thus the system's chaoticity increases. We consider a leaking soft stadium family by considering an opening limited region, located at some place of its basis's boundary, throughout which the particles can leak out. We chase the particle's trajectory and focus on the stadium transient behavior by mean of the statistical analysis of the survival probability, belonging to the marginal orbits that never leave the system, the so called bouncing ball orbits. A comparison of these family orbits is done with the billiard's transient chaos orbits.

#### Differential operators and Higher Specht polynomials

Ibrahim Nonkané1

1Université Ouaga II, Département d'Economie et de Mathématiques appliquées, IUFIC, Burkina Faso

###### Abstract

In this note, we study the action of the rational quantum Calogero-Moser system on polynomials rings. This a continuation of our paper [Ibrahim Nonkané 2021 J. Phys.: Conf. Ser. 1730 012129] in which we deal with the polynomial representation of the ring of invariant differential operators. Using the higher Specht polynomials we give a detailed description of the actions of the Weyl algebra associated with the ring of the symmetric polynomial ${\mathbb C} [x_1,\ldots,x_n]^{S_n}$ on the polynomial ring ${\mathbb C} [x_1,\ldots, x_n]$. In fact, we show that its irreducible submodules over the ring of differential operators invariant under the symmetric group are its submodules generated by higher Specht over the ring of the symmetric polynomials. We end up studying the polynomial representation of the ring of differential operators invariant under the actions of the product of the symmetric groups by giving the generators of its simple components, thus we give a differential structure to the higher Specht polynomials

#### Differential operators and reflections groups of type $B_n$

Ibrahim Nonkané1 , Latévi M. Lawson2

1Université Ouaga II, Département d'Economie et de Mathématiques appliquées, IUFIC, Burkina Faso
2African Institute for Mathematical Sciences (AIMS), Department of Mathematical Sciences, Ghana

###### Abstract

In this note, we study the polynomial representation of the quantum Olshanetsky-Perelomov system for a finite reflection group $W$ of type $B_n$. We endowed the polynomial ring ${\mathbb C} [x_1,\ldots, x_n]$ with a structure of module over the Weyl algebra associated with the ring ${\mathbb C} [x_1,\ldots,x_n]^{W}$ of invariant polynomials under a reflections group $W$ of type $B_n$. Then we study the polynomials representation of the ring of invariant differential operators under the reflections group $W$. We make use of the representation theory of groups namely the higher Specht polynomials for the reflection group $W$ to yield a decomposition of that structure by providing explicitly the generators of its simple components.

#### Differential operators and reflections groups of type $D_n$

Ibrahim Nonkané1 , Latévi M. Lawson2

1Université Ouaga II, Département d'Economie et de Mathématiques appliquées, IUFIC, Burkina Faso
2African Institute for Mathematical Sciences (AIMS), Department of Mathematical Sciences, Ghana

###### Abstract

In this note, we study the actions of Classical quantum Olshanetsky-Perelomov systems for finite reflections groups of type $D_n$. we endowed the polynomial ring ${\mathbb C} [x_1,\ldots, x_n]$ with a differential structure by using directly the action of the Weyl algebra associated with the ring ${\mathbb C} [x_1,\ldots,x_n]^{W}$ of invariant polynomials under the reflections groups $W$ after a localization. Then we study the polynomials representation of the ring of invariant differential operators under the reflections groups. We use the higher Specht polynomials associated with the representation of the reflections group $W$ to exhibit the generators of its simple components.

#### Calibration of ADCS magnetometers for space systems

Elena Rodríguez1

###### Abstract

In the present work, a method for magnetometer calibration through linearized least squares fitting is presented. This method has been developed for the magnetometers employed in the Attitude, Determination and Control Subsystem (ADCS) of UPMSat-2. The UPMSat-2 mission is a 50-kg satellite designed and manufactured by the Technical University of Madrid (Universidad Politécnica de Madrid), and finally launched in September 2020. The satellite has three fluxgate magnetometers (one of them experimental) whose calibration is critical to obtain correct measurements to be used by the ADCS. Among the several mathematical methods to obtain the calibration parameters, a linearized least squares fitting algorithm is evaluated after concluding that it is the most suitable for the presence of noise and disperse and non-homogenous data sets. The magnetometers data measured in the satellite integration test are used, along with the fitting algorithm, to obtain the sensors calibration parameters. Finally, the calibration configurations are evaluated. The results show an improvement in the accuracy of the magnetic field determination.

#### FDS simulation of smoke backlayering in emergency lay-by of a road tunnel with longitudinal ventilation

Peter Weisenpacher1

1Institute of informatics, Slovak academy of sciences, Department of Parallel Computational Methods and Algorithms, Slovakia

###### Abstract

This paper investigates smoke movement and its stratification in a lay-by of a 900 m long road tunnel by computer simulation using Fire Dynamics Simulator. The lay-by is located upstream of the fire in its vicinity. The influence of lay-by geometry on smoke spread is evaluated by comparison with a fictional tunnel without lay-by. Several fire scenarios with various tunnel slopes and heat release rates of fire in the tunnels without and with the lay-by are considered. The most significant breaking of smoke stratification and decrease of visibility in the area of the lay-by can be observed in the case of zero slope tunnel for more intensive fires with significant length of backlayering. Several other features of smoke spread in the lay-by are analysed as well. The parallel calculations were performed on a high-performance computer cluster.

###### Acknowledgements:

The authors would like to thank Peter Schmidt (National Motorway Company, Slovakia) for technical specifications of road tunnels. This work was partially supported by the Slovak Science Foundation (project No. VEGA 2/0108/20) and the Slovak Research and Development Agency (project No. APVV-15-0340).

#### Looking at quantization of wave function, from Weber(1961), from a wormhole mouth , assuming mini Quantum black holes in a worm hole mouth are Bose-Einstein Condensates of Gravitons

Andrew Beckwith1

1Chongqing University, Department of physics, China

###### Abstract

We utilize how Weber in 1961 initiated the process of quantization of early universe fields to the problem of what may be emitted at the mouth of a wormhole. While the wormhole models are well developed, there is as of yet no consensus as to how, say GW or other signals from a wormhole mouth could be quantized, or made to be in adherence to a procedure Weber cribbed from Feynman, in 1961. In doing so, we are examining arguments given in pages 181-182 by P.H. Chavanis, in "Quantum Aspects of Black holes" (Fundamental theories of physics 178) which reconcile a balance between quantum pressure( Heisenberg Uncertainty Principle) and Gravity in a wormhole mouth and secondarily in General Relativity. This involves quantum depletion of condensates (our model of black holes) by spontaneous particle emission. In doing so, we try to ascertain if wormholes may be identified via Gravitational wave astronomy

#### Geometry, Coordinatization and Cardinality of the Rational Numbers from Physical Perspectives

Kaushik Ghosh1

1Vivekananda College, Physics, India

###### Abstract

In this article, we will first discuss the completeness of real numbers in the context of an alternate definition of the straight line as a geometric continuum. According to this definition, points are not regarded as the basic constituents of a line segment and a line segment is considered to be a fundamental geometric object. This definition is in particular suitable to coordinatize different points on the straight line preserving the order properties of real numbers. Geometrically fundamental nature of line segments are required in physical theories like the string theory. We will construct a new topology suitable for this alternate definition of the straight line as a geometric continuum. We will discuss the cardinality of rational numbers in the later half of the article. We will first discuss what we do in an actual process of counting and define functions well-defined on the set of all positive integers. We will follow an alternate approach that depends on the Hausdorff topology of the real numbers to demonstrate that the set of positive rationals can have a greater cardinality than the set of positive integers. This approach is more consistent with an actual act of counting. This article indicates that the axiom of choice can be a better technique to prove theorems that use second-countability. This is important for the metrization theorems and physics of spacetime.

#### Bearing friction effect on cup anemometer performance modelling

Daniel Alfonso-Corcuera1 , Santiago Pindado2 , Mikel Ogueta-Gutiérrez3 , Ángel Sanz-Andrés4

1Instituto de Mircrogravedad "Ignacio Da Riva" (IDR/UPM), ETSI Aeronáutica y del Espacio, Universidad Politécnica de Madrid, , Spain
2Instituto Universitario de Mircrogravedad "Ignacio Da Riva" (IDR/UPM), ETSI Aeronáutica y del Espacio, Universidad Politécnica de Madrid, , Spain
4Instituto de Mircrogravedad "Ignacio Da Riva" (IDR/UPM), ETSI Aeronáutica y del Espacio, Universidad Politécnica de Madrid, , Spain

###### Abstract

In the present work, the effect of the friction forces at bearings on cup anemometer performance is studied. The study is based on two different analytical approaches to the cup anemometer behaviour. The classical one (2-cup model), used in the analysis by Schrenk in 1929 and Wyngaard in 1981, and the one based on the cups’ aerodynamics Fourier analysis (3-cup model), proposed by Pindado et al. in 2013. Results indicate a logical poorer performance (in terms of a lower rotation speed at the same wind velocity), with an increase of the friction. However, this decrease of the performance is affected by the aerodynamic characteristics of the cups. More precisely, results indicate that the effect of the friction is modified depending on the ratio between the maximum value of the aerodynamic drag coefficient (at 0º yaw angle) and the minimum one (at 180º yaw angle). This reveals as a possible way to increase the efficiency of the cup anemometer rotors.

#### On Harary energy and Reciprocal distance Laplacian energies

Macarena Trigo1

1Universidad de Antofagasta, Departamento de Matemáticas, Chile

###### Abstract

Let $G$ be an graph simple, undirected, connected and unweighted graphs. The Reciprocal distance energy of a graph $G$ is equal to the sum of the absolute values of the reciprocal distance eigenvalues. In this work, we found a lower bound for the reciprocal distance energy and reciprocal distance signless Laplacian energy of a graph. Moreover, we found relationship between the Harary energy and Reciprocal distance Laplacian energies.

###### Acknowledgements:

MINEDUC-UA project ANT20992

#### Spectral radius of the Harary matrix of the join product of regular graphs

Luis Medina1 , Macarena Trigo2

1Universidad de Antofagasta, Departamento de Matemáticas, Chile
2Universidad de Antofagasta, Departamento de Matemáticas, Chile

###### Abstract

We consider simple, undirected, connected and unweighted graphs. The distance between two vertices is equal to the number of edges on the shortest path connecting them. The Harary matrix of graph of $n$ vertices, which is also called as the reciprocal distance matrix, is an nonnegative matrix of order $n$, such that the $(i,j)$-entry is equal to the reciprocal distance between the vertices $v_i$ and $v_j$ if the vertices are different and zero if are equal. In this work we found a bound for the spectral radius of the Harary matrix of the join product of regular graphs.

###### Acknowledgements:

MINEDUC-UA project ANT20992

#### An improved Trapezoidal rule for numerical integration

Ahmed Abdulhameed1 , Qurban Memon2

1UAE University, Electrical Engineering, United Arab Emirates
2UAE University, Electrical Engineering, United Arab Emirates

###### Abstract

Numerical Methods have attracted of research community for solving engineering problems. This interest is due to its practicality and the improvement of highspeed calculations done on current century processors. The increase in numerical method tools in engineering software, such as Matlab, is an example of the increased interest. In this paper, we are present a new improved numerical integration method, that is based on the well-known trapezoidal rule. The proposed method gives a great enhancement to the trapezoidal rule and overcomes the issue of the error value when dealing with some higher order functions even when solving for a single interval. After literature review, the proposed system is mathematically explained along with error analysis. Few examples are illustrated to prove improved accuracy of the proposed method over traditional trapezoidal method.

#### An impedance approach to the response of matter

Sara Vesely1

1ITB-CNR, CNR, Italy

###### Abstract

Over time, radiation has been fitted with a number of attributes, among which energy stands out. Current mathematical theories, primarily electromagnetism, the theory of relativity, and quantum electrodynamics, are mainly concerned with two types of tasks: 1) the representation of the distribution and propagation of the electromagnetic (EM) field in physical space, which is faced by drawing on geometry, and 2) the investigation of the interaction of radiation with matter. Up until WWII, except for ionizing radiations, nobody felt the need to extend the theoretical framework beyond the perturbative approximation. Things started changing after the recent technical achievements in the generation, manipulation, and detection of radiation. Thanks to the new technologies small effects are being isolated, that were previously overlooked or unnoticed, and whose explanation demands some kind of nonlinear approach. Attempts are ongoing at explaining emergence based on statistical inference and the extant probabilistic theories. However, phenomena that on Earth take place under the influence of sunlight may manifest differently in other environments, and can be enhanced under artificial conditions. In our opinion, the classical impedance concept that is used in engineering allows a seamless shift from the geometric rendering of received electromagnetic signals (1) to the understanding of simple arguments on power transfer under matching conditions (2). It could be used to notice the occurrence of radiation-matter interactions and give hints as to how some phenomena could be enhanced by exposing matter to specific non-ionizing radiations.

#### Hilbert's 6-th problem and principle of completeness in dynamics

1Saint-Petersburg National Research University of Information Technologies, Mechanics & Optics (University ITMO), Department of Physics and Engineering, Russian Federation

###### Abstract

The following offers a new axiomatic basis of mechanics and physics in their most important dynamics domain, i.e. a principle (axiom) of completeness intended to generalize Newton's second law of motion for the case of a non-stationary variable-mass point (system) that varies with time. This generalization leads to hyperdynamic dependencies describing such motion from new accurate qualitative standpoints.

#### RAD_IQ: A free software for characterization of digital X-ray imaging devices based on the novel IEC 62220-1-1:2015 International Standard

Anastasios Konstantinidis1 , Niki Martini2 , Vaia Koukou3 , George Fountos4 , Nektarios Kalyvas5 , Ioannis Valais6 , Christos Michail7

1Portsmouth Hospitals University NHS Trust, Queen Alexandra Hospital, Department of Medical Physics, Radiological Sciences Group, United Kingdom
2University of West Attica, Biomedical Engineering, Greece
3University of West Attica, Biomedical Engineering, Greece
4University of West Attica, Biomedical Engineering, Greece
5University of West Attica, Biomedical Engineering, Greece
6University of West Attica, Biomedical Engineering, Greece
7University of West Attica, Biomedical Engineering, Greece

###### Abstract

Characterization of digital X-ray imaging devices (also known as Digital Radiography (DR) detectors) is very important because it can be used to measure and compare the performance of X-ray detectors used in Diagnostic Radiology. This characterization is usually made through the calculation of Modulation Transfer Function (MTF), Noise Power Spectrum (NPS) and Detective Quantum Efficiency (DQE). These parameters, especially the DQE, are very important because they quantify the effect of spatial resolution, contrast and noise on Radiographic image quality (IQ). The IEC 62220-1-1:2015 International Standard provides comprehensive guidelines how to capture and analyse X-ray images to characterize DR detectors. A novel, fast and free MATLAB-based software was developed, named RAD_IQ, to calculate the Signal Transfer Property (STP; also known as Response Function), perform Noise Component Analysis (NCA), and calculate the parameters MTF, NPS and DQE of DR detectors based on the novel IEC 62220-1-1:2015 International Standard. Our results were validated against well-established software products (including OBJ_IQ_Reduced) used for quantitative image quality analysis of DR detectors. The calculated parameters were within 5% difference compared to available software products. The conclusion of our study was that RAD_IQ can be easily used from Medical Physicists and Researchers without any programming experience to analyse X-ray images of DR detectors in DICOM or TIFF format.

###### Acknowledgements:

The 10th International Conference on Mathematical Modeling in Physical Sciences publication fees were funded by the University of West Attica, Greece.

#### X-ray Detection and spectral compatibility properties of Cerium Bromide (CeBr3) single crystal for medical imaging applications

Dionysios Linardatos1 , Konstantinos Velissarakos2 , Ioannis Valais3 , George Fountos4 , Anastasios Konstantinidis5 , Nektarios Kalyvas6 , Ioannis Kandarakis7 , Christos Michail8

1University of West Attica, Biomedical Engineering, Greece
2University of West Attica, Biomedical Engineering, Greece
3University of West Attica, Biomedical Engineering, Greece
4University of West Attica, Biomedical Engineering, Greece
5Portsmouth Hospitals University NHS Trust, Queen Alexandra Hospital, Department of Medical Physics, Radiological Sciences Group, United Kingdom
6University of West Attica, Biomedical Engineering, Greece
7University of West Attica, Biomedical Engineering, Greece
8University of West Attica, Biomedical Engineering, Greece

###### Abstract

Single crystal scintillators are widely used in X-ray medical imaging detector applications, coupled with suitable optical sensors. Cerium bromide (CeBr3) is a single crystal that has been previously reported with a light yield (LY) value of 60 photons/keV, which is almost 3 times the corresponding LY value of other promising materials, such as lutetium aluminium garnet (LuAG:Ce - Lu3Al5O12:Ce (LY=25photons/keV), thus it would of worth to examine its X-ray detection properties for medical applications. In this study the X-ray absorption properties of CeBr3 single crystals, as well as its spectral compatibility with numerous optical sensors were investigated. The quantum detection (QDE) and the energy absorption efficiency (EAE) of a CeBr3 single crystal, (10x10x10 mm3) were calculated using coefficients of total-attenuation and energy-absorption from the national institute of standards and technology (NIST) regarding cerium (Ce) and bromine (Br), using the XmuDat photon attenuation database software. Spectral data up to 140 kV was simulated using Siemens X-Ray spectra simulation software. Results were evaluated against published data of our team, for single crystals of equal dimensions (CaF2:Eu and Lu3Al5O12:Ce). The spectral matching, between the optical spectrum emitted by CeBr3 and the spectral sensitivity of various optical sensors were calculated using the measured optical spectrum and published data for the spectral sensitivities. EAE values of CeBr3 were found higher than both CaF2:Eu and Lu3Al5O12:Ce when the energy increases more than 100kVp, whereas the QDE values were constantly equal to 1, up to 100kVp. The light emitted from CeBr3 can be optimally detected by photocathodes, such as gallium arsenide (GaAs) (94%), extended photocathode (E-S20) (95%), with position sensitive photomultipliers (PS-PMT), flat panel PS-PMT H8500C-03 (99%), PS-PMT H8500C (97%), multialkali photocathodes (97%) and bialkali photocathodes (95%). Conclusions: Despite the intermediate density value (5.1 g/cm3) of CeBr3 and its hygroscopicity, the detection and absorption results of this material make it suitable for medical imaging applications.

###### Acknowledgements:

The 10th International Conference on Mathematical Modeling in Physical Sciences publication fees were funded by the University of West Attica, Greece.

#### Darboux transformations for Dirac equations with arbitrary diagonal potential matrix in two dimensions

Axel Schulze-Halberg1

1Indiana University Northwest, Department of Mathematics and Actuarial Science, United States

###### Abstract

We construct Darboux transformations for the two-dimensional Dirac equation with a diagonal matrix potential. The potential is allowed to depend arbitrarily on both variables. The scenario of a position-dependent mass as well as the massless case are included.

#### The atomic structure of chemical elements in the theory of compressible oscillating ether

Nikolai Magnitskii1

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

###### Abstract

Previously, the basic laws and equations of electrodynamics, atomic nuclei, elementary particles theory and gravitation theory were derived from the equations of compressible oscillating ether [1-4]. In this work, the theory of atomic structure for all chemical elements is constructed. A formula for the values of the energy levels of the electrons of an atom, which are the values of the energies of binding of electrons with the nucleus of an atom in the ground unexcited state, is derived from the equations of the ether. Based on experimental data on the ionization energies of atoms and ions, it is shown that the sequence of values of the energy levels of electrons has jumps, exactly corresponding to the periods of the table of chemical elements. It is concluded that it is precisely these jumps, and not quantum-mechanical rules, prohibitions and postulates that determine the periodicity of the properties of chemical elements. Ethereal correction of the table of chemical elements is presented which returns it to the form proposed by D.I. Mendeleev. 1. Magnitskii N.A. Theory of compressible oscillating ether. Results in Physics, 12 (2019), p.1436–1445. 2. Magnitskii N.A. Fundamentals of the theory of compressible oscillating ether. IOP Conf. Series: Journal of Physics: Conf. Series 1141 (2018) 012052. 3. Magnitskii N.A. Structure and properties of atomic nuclei in the theory of compressible oscillating ether. IOP Conf. Series: Journal of Physics: Conf. Series 1391 (2019) 012084. 4. Magnitskii N.A. Gravitation in the theory of compressible oscillating ether. IOP Conf. Series: Journal of Physics: Conf. Series 1730 (2021) 012012

#### Bounds on spectral radius of Harary matrix

Luis Medina1

1Universidad de Antofagasta, Departamento de Matemáticas, Chile

###### Abstract

We consider simple, undirected, connected and unweighted graphs. The distance between two vertices is equal to the number of edges on the shortest path connecting them. The Harary matrix of graph of $n$ vertices, which is also called as the reciprocal distance matrix, is an nonnegative matrix of order $n$, such that the $(i,j)$-entry is equal to the reciprocal distance between the vertices $v_i$ and $v_j$ if the vertices are different and zero if are equal. The spectral radius of a square matrix is the largest absolute value of its eigenvalues. In this work we find bounds for the spectral radius of the Harary matrix in terms of other graph invariants.

#### On spectral radius of Reciprocal distance signless Laplacian matrix

Luis Medina1

1Universidad de Antofagasta, Departamento de Matemáticas, Chile

###### Abstract

The reciprocal distance degree of a vertex $v$ is equal to sum of the reciprocal distance between the vertices $v$ and all the other vertices of the connected graph. The Reciprocal Distance signless Laplacian matrix of a simple, undirected, connected and unweighted graph on $n$ vertices, is an $n\times n$ matrix such that the $i$-th diagonal entry is equal to the reciprocal distance degree of a vertex $v_i$ and the $(i,j)$-entry is equal to the reciprocal distance between the vertices $v_i$ and $v_j$ if the vertices are different. The spectral radius of a square matrix is the largest absolute value of its eigenvalues. In this work, we show results on the spectral radius and we find bounds for the spectral radius of the Reciprocal Distance signless Laplacian matrix.

#### Crossover from BKT-Rough to KPZ-Rough Surfaces for Crystal Growth or Recession

Noriko Akutsu1

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

###### Abstract

We found a crossover from a Berezinskii-Kosterlitz-Thouless (BKT, logarithmic)-rough surface to a Kardar-Parisi-Zhang (KPZ, algebraic)- rough surface for growing or receding vicinal crystal surfaces in the non-equilibrium steady state using the Monte-Carlo method [1]. The adopted model is a restricted solid-on-solid (RSOS) model with a discrete Hamiltonian, $${\mathcal H}=\sum_{\{m,n\}} \left\{\epsilon[|h(m+1,n)-h(m,n)| \right.$$ $$+ |h(m,n+1)-h(m,n)|]$$ $$- \Delta \mu \ h(m,n)\} + {\mathcal N} E_{{\rm surf}},$$ where $h(m,n)$ is the height of the surface at a site $(n,m)$, $\epsilon$ is the microscopic ledge energy, ${\mathcal N}$ is the total number of unit cells on the (001) surface, $\Delta \mu$ is a driving force for crystal growth [2], and $E_{{\rm surf}}$ is the surface energy per unit cell. Here, “restricted” means that the surface-height difference between nearest-neighbour sites is restricted to 0, and ±1. The vicinal surfaces are tilted between the (001) and (111) surfaces.
We also found that the crossover point from a BKT-rough surface to a KPZ-rough surface is different from the kinetic roughening point [3] for the (001) surface. Multilevel islands and negative islands (island-shaped holes) on the terrace formed by the two-dimensional nucleation process are found to block surface fluctuations, which contributes to making a BKT-rough surface.

[1] Akutsu, N. Sci. Rep. 2020, 10, 13057, 1‒11.
[2] Widom, B. Statistical Mechanics: A Concise Introduction for Chemists; Cambridge University Press: London, UK, 2002.
[3] Wolf, D.E. Phys. Rev. Lett. 1991, 67, 1783‒1786.

###### 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 of the Research Institute for Applied Mechanics, Kyushu University.

#### Fractal behaviors of networks induced on infinite tree structures by random walks

Nobutoshi Ikeda1

1Tohoku Seikatsu Bunka Junior College, Living and Culture, Japan

###### Abstract

Fractality is a universal property found in real networks, including the World Wide Web, social networks, and biological networks. Recent studies on model networks have revealed that random processes occurring on networks could be one mechanism that induces the fractal properties of the networks. Fractal networks induced on tree graphs by movements of random walkers [Ikeda N 2020 Physica A 537, 122743] is a typical example demonstrating the ability for a random process on a network to generate fractality. In the model, tree graphs like Cayley trees provide a stage to support the self-organization of fractal networks by the flow of walkers from the root vertex to the outermost shell of the tree graph. However, the finite scale of the tree structure assumed in the model restricts the size of fractal networks. In this paper, we remove the restriction on the size of the trees by introducing a lifetime $\tau$ (number of steps of random walks) of walkers. As a result, we have succeeded in inducing a size-independent fractal structure onto a tree graph without a boundary. The elimination of the size effect allows comprehensive investigation of the properties of the model networks. Our numerical results show that the mean number of offspring $n_{\rm b}$ of the original tree structure determines the value of the fractal box dimension $d_{\rm b}$ through the relation $d_{\rm b}-1 = (n_{\rm b} -1)^{-\theta}$. The lifetime $\tau$ controls the presence or absence of the small-world and the scale-free property. Ideal fractal behavior can be maintained by selecting an appropriate value of $\tau$. Our numerical results contribute to the development of a systematic method of generating fractal small-world scale-free (or non-small-world non-scale-free) networks while controlling the value of fractal box dimension. Unlike other models using recursive rules generating similar structures, this model specifically produces scale-free and fractal networks with the small-world property.

#### Dissociation and recombination in the electrolyte flow model

Andrey Shobukhov1 , Hiroshi Koibuchi2

1Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics, Russian Federation
2National Institute of Technology (KOSEN), Sendai College, , Japan

###### Abstract

We study a one-dimensional model for the electrokinetic flow of the dilute aqueous NaCl solution. It is regarded as an incompressible fluid placed in the external electric field. The model is based on the Poisson-Nernst-Planck system of equations. The model also takes into account the dissociation and the recombination of the ions and contains the constant flow velocity as a parameter. We compare the variants with and without diffusion. The steady state solution is investigated analytically; it is proved to be the stable equilibrium for all parameter values. We analyze the numerical solutions and demonstrate the importance of including the processes of dissociation and recombination.

#### Mathematical Modeling of Soliton-Like Modes at Optical Rectification

Aleksey Kalinovich1 , Irina Zakharova2 , Sergey Sazonov3 , Maria Komissarova4

1M.V.Lomonosov Moscow State University, Faculty of Physics, Russian Federation
2M.V.Lomonosov Moscow State University, Faculty of Physics, Russian Federation
3National Research Centre "Kurchatov Istitute", , Russian Federation
4M.V.Lomonosov Moscow State University, Faculty of Physics, Afghanistan

###### Abstract

We discuss the results of numerical modeling of forming optical-terahertz bullets at the process of optical rectification. Our calculations are based on a generalization of the well-known Yajima - Oikawa system, which describes the nonlinear interaction of short (optical) and long (terahertz) waves. The generalization relates to situations when the optical component is close to the few-cycle pulse. Our previous studies of the considered process indicate a tendency to improve the conditions for the formation of spatiotemporal optical terahertz solitons in a waveguide with a decrease in the number of oscillations of the optical component. Given this trend, in the present investigation we conduct a finer accounting of the influence of the number of optical pulse oscillations on the generation of a terahertz signal. To this end we use as a mathematical model a more complicated system introduced earlier. We developed original nonlinear conservative pseudo-spectral difference scheme approximating the generalization of the Yajima-Oikawa system. It is realized with the help of FFT algorithm. Mathematical modeling demonstrates scheme effciency.

###### Acknowledgements:

Work was supported by Russian Science Foundation (Project No. 17-11-01157).

#### Numerical Solutions of Generalized Newtonian Fluids Flow for Different Bypass Geometry

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

###### Abstract

This paper deals with the numerical simulation of generalized Newtonian fluids flow in the different bypass geometry. The considered geometry consists of the narrowed main tube and the bypass graft. The quality of the blood flow in the bypass can be influenced by a location of the narrowing or by the geometry. The optimal angle for the connecting of the bypass graft to the vessel is around 45 degrees, therefore this work is mentioned on the numerical modelling of the varied mathematical models of the viscosity with the angle of the connection 45 and 60 degrees. Our study is focused on testing different types of bypass geometry, standard and S-type bypass connections. As well as various narrowing of the problematic section in the main channel are presented. Symmetrical and unsymmetrical narrowing is tested for both types of bypass. The governing system of equations is based on the system of balance laws for mass and momentum. Generalized Newtonian fluids flow in the bypass is numerically simulated by using open source CFD tool, OpenFOAM with a SIMPLE algorithm.

###### Acknowledgements:

This work was supported by the grant agency of the Czech Technical University in Prague, grant No. SGS19/154/OHK2/3T/12.

#### Non-smooth Modeling and Variable Structure Control of a Class of Hybrid Dynamical Systems

Yasser Bin Salamah1

1King Saud University , ELECTRICAL ENGINEERING, Saudi Arabia

###### Abstract

In this work, we propose a modeling formulation and controller design for a class of hybrid dynamical systems. In this formulation, a switching dynamical system is modeled as a dynamical system with discontinuous right hand side. More specifically, the system is transformed to a nonlinear system with discontinuous nonlinearities. Then, a synthesis of feedback linearization and sliding mode control is employed for output tracking control problem. Application and implementation of this approach is illustrated via a chemical process example.

#### A Physical Action Principle for Biological Systems

Richard Summers1

1University of Mississippi Medical Center, Office of Research, United States

###### Abstract

Background: Instead of considering the direct forces and mechanisms for change codified in the Newtonian laws of physics, the rederivation of phenomena by Lagrange and Hamilton emphasized the identification of the right action principle as a more general framework for dynamics. For the living system, it is the experiential establishment of the biocontinuum’s dimensional structure that creates the meaningful information for directing the action dynamics of any phenomena. By driving actions for system adaptation, this dynamic information processing also serves as a general action principle for the living systems. Methods: A nonequilibrium thermodynamic steady state is considered as the base state for all living systems with any deviations from this condition resulting from some force for change. For living systems that autonomously determine their own attractor conditions, the process of acquiring experiential information and translating it into actionable meaning for adaptive responses becomes the action dynamic for the system change. Therefore, the core axiomatic structure of this experiential process should include an innate general action principle that can determine the system directional changes without requiring a detailing of the particulars of the system. Adaptive changes within any complex living system is then naturally mapped by the information geometry of its experiential biocontinuum space and the resultant Lagrangian of that space. Results: A mathematical expression incorporating the natural entropy driven Kullback Principle of Minimum Information Discrimination (KLD) and nonlinear system replicator dynamics that describes biologic information processing can serve as an action functional for living systems. This information entropic dynamic path guided by the KLD along a geodesic trajectory naturally minimizes the distances between information points in the biocontinuum as a least action principle and serves as an inference procedure for directional system change. Expressions for the potential and kinetic information of the biocontinuum are then defined by: I(q,p)=∑_i^n▒〖ln⁡(q_i/p_i ) q_i 〗=∑_i^n▒〖[ln (q_i)〗⁡〖- ln 〖(q〗_i)] q_i 〗 and d/dt I(q,p)=-∑_i^n▒〖[f_i 〖(P)-f(P)]q〗_i 〗= ∑_i^n▒〖f_i 〖(P)(p_i-q〗_i) Where I(q,p) is the information state and q is a target goal state with a fixed probability distribution and p is time dependent probabilities of current state. The fitness fi(P of each type i in the population is a likelihood probability characteristic in the context of the environment. Then the Action (S) is defined as the integral summation of the Lagrangian integrand as the difference between the kinetic and potentials at each phase of the change transition of the phenomena which is minimized by KLD during the trajectory of the dynamics. $Action=S=∫_(t_1)^(t_2)▒〖(KE- PE)dt〗$ Conclusion: The drive for adaptive system reconciliation of any divergence from the steady state condition within the biocontinuum can be described by a mathematical formulation of the experiential process. This process for actionable knowledge acquisition incorporates an axiomatic inference of Kullback-Leibler information minimization driven by natural entropy forces and operated by survival replicator dynamics. If this mathematical expression of the experiential process is the Lagrangian integrand for adaptive change in the biocontinuum then it can also be considered as a general action principle and functional for the living system.

#### Estimation of the trajectories of magnetic nanoparticles in non-newtonian vascular fluid using neural networks

Israel Contreras Rodríguez1 , Diego Barragán Vargas2 , Luz H Camargo3

1Universidad Distrital Francisco José de Caldas, Faculty of Engineering, Colombia
2Universidad Distrital Francisco José de Caldas, Faculty of Engineering, Colombia

###### Abstract

Treatments to combat cancer seek to reach specific regions to ensure maximum efficiency and reduce the possible adverse effects that occur in the treatment. One of these strategies includes the treatment with magnetic nanoparticles (NPM), which has presented promising results, however, aspects involved in the trajectory of the nanoparticles are not yet known. The objective of this work consisted of estimating the behavior of NPM through supervised neural networks, for this, artificial neural networks were implemented, such as multilayer perceptron, with optimization algorithms in which the Levenberg Marquardt algorithm stands out, different trajectories of NPM were simulated in coronary arteries, including parameters such as time, position in X and Y, the velocity that the nanoparticles can reach and physical factors that interact in the distribution were considered, such as the gravitational field, the magnetic field, the Stokes force, the force of pushing and dragging with different values of viscosity in the blood, generating a database with optimized reaction times that allow a more accurate prediction. The architecture obtained with the artificial neural network that contains the optimization algorithm [5 4 3 2], presented the best performance with a training MSE of 1.763E-07, a validation uRMSE of 0.0049 and trend probabilities of 0.62 in X and 0.576 in Y.

#### The longtime global climatic consequences modeling of the Chicxulub asteroid impact event

Valeriy Parkhomenko1

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

###### Abstract

Studies indicates the mass death of a significant number of biological groups on Earth, in particular - dinosaurs, at the end of the Cretaceous period 66 million years ago. Currently, there are two main theories: large-scale volcanic eruptions and the asteroid impact that formed the Chicxulub crater (Mexico). The production of sulfur-containing gases from the Earth's surface layers vapors during impact is considered a main source of climatic effects, as they form stratospheric sulfate aerosols that block sunlight and thus cool the Earth's atmosphere and interfere with photosynthesis. It is presented an application of the 3-D coupled global hydrodynamic climate model of intermediate complexity, including ocean model, sea ice evolution model and energy - moisture balance atmosphere model to study this asteroid impact effects on the Earth's climate. The model continents and ocean depths distribution corresponds to Cretaceous period. A series of calculations with different residence times and deposition times of the stratosphere aerosol have been carried out. It was found that, depending on the stratosphere aerosol time parameteres, the global annual average surface air temperature decreased by 18°С - 27°С, remained below zero for 4 - 30 years, and a recovery time of more than 30 years was observed. For a aerosol deposition time of 3 years in the stratosphere, which is the most conservative modeling assumption, the global mean annual surface air temperature decreases by 27°C, with a minimum temperature reached 3rd year after impact. The air temperature remains below zero for 5 years. For deposition times of 5 and 10 years, the minimum global mean annual surface air temperature is even lower. The cooling after impact is accompanied by a noticeable expansion of the snow and sea ice area. For a aerosol deposition time of 3 years, the sea ice area increases by 30% and then slowly decreases to its original value. For a aerosol deposition time of 10 years, the sea ice area increases sharply after the initial cooling period (maximum 4 times after about 25 years), which indicates the beginning of a process caused by a positive ice-albedo feedback. On the 30th year after the impact, strong surface cooling leads to very cold water masses in the upper 1000 m at all latitudes and up to the ocean floor at high latitudes. The CO2 release from the impact will result in warming compared to the pre-impact state after the initial cooling period.

#### Modelling and numerical simulation of the TASEC-Lab power subsystem

Sergio Marín-Coca1 , David González-Bárcena2 , Santiago Pindado3 , Elena Roibás-Millán4

1Instituto Universitario de Mircrogravedad "Ignacio Da Riva" (IDR/UPM), ETSI Aeronáutica y del Espacio, Universidad Politécnica de Madrid, , Spain
2Instituto Universitario de Mircrogravedad "Ignacio Da Riva" (IDR/UPM), ETSI Aeronáutica y del Espacio, Universidad Politécnica de Madrid, , Spain
3Instituto Universitario de Mircrogravedad "Ignacio Da Riva" (IDR/UPM), ETSI Aeronáutica y del Espacio, Universidad Politécnica de Madrid, , Spain
4Instituto Universitario de Mircrogravedad "Ignacio Da Riva" (IDR/UPM), ETSI Aeronáutica y del Espacio, Universidad Politécnica de Madrid, , Spain

###### Abstract

This paper describes the modelling and simulation of the Electrical Power Subsystem (EPS) of the Thermal Analysis Support and Environment Characterization Laboratory (TASEC-Lab). TASEC-Lab is a university experiment on board a sub-orbital platform. It is designed to measure the convection heat transfer in high-altitude balloon missions. The EPS provides, regulates and distributes electric power to the different systems, parts and sensors that compose the TASEC-Lab (e.g., On Board Computer (OBC), temperature and pressure sensors, cup anemometer, GPS, heaters…). It mainly consists of a Li-ion battery and two DC-DC converters, and they have been characterized by conducting laboratory tests and fitting to experimental data. A real power consumption profile of the first TASEC-Lab’s mission (designed by Universidad Politécnica de Madrid) is used as input to simulate the EPS. The mathematical model is validated by comparison with experimental results.

###### Acknowledgements:

The authors are grateful for the support of the IDR/UPM Institute staff and the UPM students involved in the TASEC-Lab project.

#### Analysis of chosen numerical methods for the application in high order interior ballistics simulations

Marcin Krol1

1Military Institute of Armament Technology, Department of Ballistics, Poland

###### Abstract

Considering constant development of the interior ballistics, along with new gun and ammunition designs, the necessity of in-depth analysis of the shot event is continuously increasing. Numerical simulations of interior ballistics problems are useful for optimising new designs as well as explaining complex issues, regarding performance instabilities or catastrophic failures. With the rise of the computing power, there is a significant urge to drive the numerical errors towards machine zero. This goal demands using methods of high order of accuracy in both space and time. Current methods allow to achieve an arbitrary order of numerical accuracy, thus allowing to shift the focus towards sophistication of the mathematical model of the studied phenomenon. Therefore, in this work, some numerical schemes, in the context of finite volume method, are reviewed and studied using well established test problems. The results of the presented analysis are meant to become the basis for future development of a high order numerical scheme for simulation of interior ballistics problems.

#### FPGA Based Robotic Arm Controller Using Verilog HDL Programming

Fazal Noorbasha1

1K L University, Electronics & Communication Engineering, India

###### Abstract

This paper describes the building of robotic arm and wheel which is used to execute several operations with correctness with six degrees of choice. A robotic arm is a usually programmable mechanical arm, which can be used to pick and place various objects in the industries from one place or position to another place or position. It may be the addition of the mechanism or may be part of a more multifaceted robot. The parts of these manipulators or arms are interconnected through articulated joints that allow both a move and rotational movement. The FPGA based project is implemented using Spartan3 FPGA. The vital design gives independence to the robot i.e. avoiding the collision with substance and generates possible moving path.

#### A Novel Binary Encryption and Decryption Process using NAND-NOR Linear Convolution Technique

Fazal Noorbasha1

1K L University, Electronics & Communication Engineering, India

###### Abstract

The main concern in this research topic is to provide security in binary digital data in communication process. Security is one of the leading challenges usually encountered in electronic systems and this causes a major problem in the data transmission and reception. Safe and sound communications are essential for the efficient data operation techniques to assure that no intruder can gain access to the information being transmitted. During the process of encryption and decryption of the data some unique keys are employed in order to encrypt and decrypt the data. In order to implement this we have realized a novel NAND-NOR linear convolution technique. In this work we have implemented an algorithm for 4-bit input data encrypted with 4-bit key finally a 20-bit encrypted data will be transmitted. Data encryption is done by NAND Linear Convolution Process. At receiver end 4-bit information data will be decrypted from 20-bit encrypted data. Data decryption is done by NOR Linear Convolution Process. FPGA system was modeled and synthesized using Verilog HDL (Hardware Description Language).

#### FPGA based COVD testing system

Fazal Noorbasha1

1K L University, Electronics & Communication Engineering, India

###### Abstract

The global outburst of the Corona Virus Disease 2019 (COVID-19) pandemic has uncovered the fragility of health care and public health preparedness and planning against the pandemic. It has amazed the world with its quick speed, probable virulence, with a potentially profound overall shock on the lives of people from together a safety and an economic perspective. Therefore an effective assessment strategy is vital to maximizing the tested population and social distancing in a short sum of time. This article proposes an FPGA based device to detect the corona various in the pandemic.

#### A new method to integrate N-body dynamics with different interaction potentials.

Roberto Capuzzo Dolcetta1

1Sapienza, University of Rome, Dipartimento di Fisica, Italy

###### Abstract

We present our new method of integration of the motion of a set of "particles" interacting with a pair potential. The method, called "bizarre", bases on the approximation of the interaction potential via a step-wise function whose precision is arbitrarily high. Rather than aiming to a detailed study of the development of individual trajectories, our method aims to obtain robust and significant results on statistical properties of the systems under study. Testing of our implemented algorithm based on this approach has been performed choosing different interaction potentials: - the classic Newtonian gravitational potential (scale-free and decaying as the mutual distance between a given pair of massive particles); - a typical inter atomic potential, like for instance the Lennard-Jones potential.

#### The study of the dynamics for electorate system by using q-distributions-a case study.

Dode Prenga1 , Klaudio Peqini2 , Rudina Osmanaj3

1University of Tirana, Physics, Albania
2University of Tirana, Physics, Albania
3University of Tirana, Physics, Albania

###### Abstract

Abstract. In this work we have analyzed the electorate system in Albania by utilizing the distributions of the subjects that have gathered a given proportion of the votes. By exploring the features of the macro state expressed in the emerging distributions, we aimed the identification of the dominant factors playing at the micro level of electoral agreement. Herein we obtained that for the majority-like or strongly polarized voting processes, the distributions based on the voting station data showed a two-pieces objects, and each part belongs to a specific group of subjects or candidates mostly supported by the so-called green electorate or rational voters. When using the data from the electoral units that include many voting centers, the scoop upside down -looking distributions are transformed onto the deformed q-exponential and q-gaussians. It indicates that the competition between the preferential attachment and zealotry effect mechanisms is easy observable for those small size networks, but loose its importance by the aging of the network or increasing of its size. For the less polarized voting process where we qualified the voting for administrative councils and the voting for the candidates in the legislative election with semi-opened lists in 2021, the distributions are made up of two exponentials or deformed q-gaussians for all election results references, indicating the presences of a failures or structural defects in the corresponding opinion networks. We connected this finding with the effect of un-absorbable complex electoral rules, mechanically attributed votes including the inertia the first listed candidates, and other causes that are not related with mechanisms of link establishing or opinion formation. Also, electorate networks might have suffered extra irregularity issues due to the un-appropriate sizes of elections units., etc. Next, by employing the results of the two big parties, the evaluated distributions are identified as q-gaussians with 15/3, we have proposed and endorsed some prediction for the future behavior of corresponding sub-systems assuming the relaxation processes that would push the distributions toward more stationary q-gaussians. Collecting the observed properties and revealed features of the socio-physical system under scrutiny hereby, we have underlined the more significant characteristics as the non-stationarity degree of the electorate states, the persistent behavior of green electorate for last successive elections, and the presence of the small size-effect defects on the network. Based on those remarks, we have proposed the use of the q-utility function to correct the electoral opinion mechanisms, aiming on a deterministic interpretation of the observed properties. In this ad hoc model, the bias parameter in the preferential attachment model is proposed to be the prior agreement evaluated by the q-XY opinion model that we have introduced recently.

#### EPR and Optical Absorption Studies of Cu2+ ions doped ZnAlBiB Glasses

M V V K Srinivas Prasad1

1K L E F (Deemed to be University), Physics, India

###### Abstract

Copper ions doped Zinc Alumino Bismuth Borate (ZnAlBiB) glasses with different concentrations of copper ions were characterised by using FT-IR, electron paramagnetic resonance (EPR) and optical absorption studies. The FT-IR spectra show various stretching and bending vibrations of ZnAlBiB glasses. The EPR spectra of all these glasses reveal a resonance signal, characteristic of Cu2+ ions in axially elongated octahedral sites. The values of the spin-Hamiltonian parameters indicate that the Cu2+ ions in these glasses are present in octahedral coordination with tetragonal distortion. With the increase of the copper ion it is found that the g_⊥ component increases. The optical absorption of all the glasses shows a single broad band. By correlating EPR and optical absorption data, the molecular orbital coefficients have been evaluated. The optical band gap energy (Eopt) and Urbach energy (∆E) are calculated at ultraviolet edges. It is found that as the copper ion concentration increases the optical band gap decreases and the Urbach energy increases.

#### Energy-Variation Analysis and Orbit Complexity Quantification

Fotios Kasolis1

1University of Wuppertal, Chair of Electromagnetic Theory, Germany

###### Abstract

Commonly, in standard recurrence analysis, recurrences are considered either in the space that constitutes of the observed quantities, or in an embedding space that is manufactured by time-delayed variables. An alternative approach is proposed here. In the so-called energy-variation analysis, the complexity of an orbit is quantified in terms of the statistics of the constant-speed geodesic condition. Energy-variation analysis requires significantly less operations than recurrence analysis, in particular, for multivariate time-series, while numerical experiments demonstrate that the resulting matrix encodes information that is sufficient for quantifying the complexity of an orbit.

###### Acknowledgements:

This work was supported in parts by the Deutsche Forschungsgemeinschaft (DFG) under grants no. CL143/11-2 and CL143/18-1.

#### AN INVENTORY MODEL FOR PRICE SENSITIVE DEMAND AND VARYING HOLDING COST FOR DETERIORATING ITEMS

Uttam Kumar Khedlekar1

1Dr Harisingh Gour Vishwavidyalaya, Sagar MP India-470003, Mathematics, India

###### Abstract

This paper presents an inventory model with linear function demand of time and price. The coefficient of time-parameter and coefficient of price-parameter are examined simultaneously and proved that time is dominating variable over price in terms of earning more profit. The robustness of the suggested model is examined using variations in the input parameters. Two kinds of doubly-demand function strategies are examined and mutually compared in view of the two different cases. Second strategy found better than first. Holding cost is treated as a variable. Some recommendations are given at the end for the inventory managers and also open problems are discussed for researchers. This model is more realistic than considered by earlier author.

###### Acknowledgements:

I acknowledge to Prof Diwaker Shukla, Dr. Harisingh. Gour Vishwavidyalayas, Sagar, M.P., India.

#### Scaling laws and phase space analysis of a geomagnetic domino model

Klaudio Peqini1 , Dode Prenga2 , Rudina Osmanaj3

1University of Tirana, Physics, Albania
2University of Tirana, Physics, Albania
3University of Tirana, Physics, Albania

###### Abstract

The geomagnetic field is among the most striking features of the Earth. By far the most important ingredient of it is generate in the fluid conductive outer core and it is known as the main field. It is characterized by a strong dipolar component as measured on the Earth's surface. It is well established the fact that the dipolar component has reversed polarity many times, a phenomenon dubbed as dipolar field reversal (DFR). there have been proposed numerous models focused on describing the statistical features of the occurrence of such phenomena. One of them is the domino model, a simple toy model that despite its simplicity displays a very rich dynamics. This model incorporates several aspects of the outer core dynamics like the effect of rotation of Earth, the appearance of convective columns which create their own magnetic field, etc. In this paper we analyze the phase space of parameters of the model and identify several regimes. The two main regimes are the polarity changing one and the regime where the polarity remains the same. also we draw some scaling laws that characterize the relationship between the parameters and the mean time between reversals (mts), the main output of the model.

#### Generalized IBL models for gravity-driven flow over inclined surfaces

Serge D'Alessio1 , Jon-Paul Mastrogiacomo2 , Jean-Paul Pascal3

1University of Waterloo, Centre for Education in Mathematics and Computing, Canada
2University of Waterloo, Faculty of Mathematics, Canada
3Ryerson University, Department of Mathematics , Canada

###### Abstract

In this investigation we propose several generalized first-order integral-boundary-layer (IBL) models to simulate the two-dimensional gravity-driven flow of a thin fluid layer down an incline. Various cases are considered and include: isothermal and non-isothermal flows, flat and wavy bottoms, porous and non-porous surfaces, constant and variable fluid properties, and Newtonian and non-Newtonian fluids. A numerical solution procedure is also proposed to solve the various model equations. Several results from our numerical experiments will be presented. To validate the generalized IBL models comparisons were made with existing results and the agreement was found to be reasonable.

###### Acknowledgements:

Financial support for this research was provided by the Faculty of Mathematics at the University of Waterloo and the Natural Sciences and Engineering Research Council of Canada.

#### Determining the best set of Molecular Descriptors for a Toxicity Classification Problem

###### Abstract

The safety norms for drug design are very strict with at least three stages of trials. One test, early on in the trials, is about the cardiotoxicity of the molecules, that is, whether the compound blocks any heart channel. Chemical libraries contain millions of compounds. Accurate \textit{a priori} and \textit{in silico} classification of non-blocking molecules, can reduce the screening for an effective drug, by half. There are other risk factors that the compound needs to be checked for alongside its therapeutic effect. Actual screening in a research laboratory is very expensive and time consuming. These tests can also be done using a computer. For this purpose, the molecules are provided in Simple Molecular Input Line Entry (SMILE) format. In this study, they have been decoded using the chem-informatics development kit written in the Java language. The kit can be accessed in the R statistical software environment through the \textit{rJava} package, that is further wrapped in the \textit{rcdk} package. The strings representing the molecular structure, are parsed by the \textit{rcdk} functions, to provide structure-activity descriptors, that are known, to be good predictors of biological activity. These descriptors along with the known blocking behaviour of the molecule, constitute the input to the Decision Tree, Random Forest, Gradient Boosting, Support-Vector-Machine, Logistic Regression, and Artificial Neural Network algorithms.

###### Acknowledgements:

Kunal Roy, from Jadavpur University, piqued our interest in the classification problem, by sharing the dataset at the onset of the public health crisis. Rajarshi Guha, at the National Institute of Health (NIH), Maryland, USA, was supportive, about the usage of the rcdk package.

#### Space-time breather solution for system of nonlinear Klein-Gordon equations

Yoritaka 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 nonlinear Klein-Gordon equations, their breather solutions are usually known as time periodic solutions with the vanishing spatial-boundary condition. The existence of breather solution is known only for a limited cases of nonlinear Klein-Gordon equations. The breather solution is a certain kind of time periodic solutions that are not only play an essential role in the bridging path to the chaotic dynamics, but provide multi-dimensional closed loops inside phase space. In this paper, based on the high-precision numerical scheme, the appearance of breathing mode is studied for a system of nonlinear Klein-Gordon equations with spatial boundary condition, where the space-time breather solutions of Klein-Gordon equations are expected to be fundamental building blocks of the sub-atomic nonlinear dynamics. The competition, coherence, and decoherence of different waves are shown to appear depending on the choice of parameter values. In conclusion, the conditional existence of space-time periodic breather solution is presented, and the compact manifolds inside the infinite-dimensional dynamical system is shown.

#### The Room Allocation Optimization Problem in Examination Timetabling – a New Model and a New Heuristic

Ahmad Datti1 , Abdulwahab Lawan2 , Ibrahim Yusuf3

1Bayero University Kano, Computer Science, Nigeria
2Bayero University Kano, Information Technology, Nigeria
3Bayero University Kano, Mathematical Sciences, Nigeria

###### Abstract

The room allocation problem is an NP-Hard optimization problem found in many resource allocation problems such as the exam timetabling problem. Due to the real-life setting of the timetabling problems studied in existing literature, the room allocation problem has been solved by simple algorithms. This is mainly because the problem has been constrained by only room capacity. In this research, a new complex room allocation problem whose rooms are spread across a very wide geographical area is studied. The solution requires having each student placed in a room close to his or her department to minimize the cost of movement on the students and avoid stress and anxiety related to unfamiliar rooms. A new optimization model and constructive heuristic for this problem are proposed. A genetic algorithm was employed in finding an optimal solution using a new optimization model and a new constructive heuristic. Experiments have shown the superiority of the proposed heuristic compared to simple random allocation of students by about 43% improvement in solution fitness. This indicates that our proposed heuristic is very suitable for solving these kinds of problems.

#### Computational Absorption and Reflection Studies of Human Cornea Exposed to Millimetre Wave Radiation at 30 and 60 GHz

Negin Foroughimehr1 , Zoltan Vilagosh2 , Andrew Wood3

1Swinburne University of Technology, Health Sciences, Australia
2Swinburne University of Technology, Health Sciences, Australia
3Swinburne University of Technology, Health Sciences, Australia

###### Acknowledgements:

This research is partially funded by the National Health and Medical Research Council (Grant# 1042464).

#### Modeling of the content of the physics course based on the percolation coefficient

Alexey Tsoy1

1FEFU, Department of General and Experimental Physics, Russian Federation

###### Abstract

This article discusses the possibility of modeling the connected content of physics courses and mathematical analysis by establishing the percolation coefficient. A research is carried out for the basic concepts of mathematics selected using a graph model of intersubject connections (Gnitetskaya T. N.). It is assumed that the value of the coefficient will increase with an increase in their connectivity.

#### A machine learning approach of finding the optimal anisotropic SPH kernel

Eraldo Marinho1

###### Abstract

It is presented a machine learning approach to find the optimal anisotropic SPH kernel, whose compact support consists of an ellipsoid that matches with the convex hull of the self-regulating k-nearest neighbors of the smoothing particle (query).

#### Mathematical modeling of drug-diffusion from multi-layered capsules/tablets and other drug-delivery devices

Saqib MUBARAK1

1University of Kashmir, Mathematics, India

###### Abstract

In this paper, two mathematical models have been formulated, in light of the basic reaction-diffusion model along with reasonable initial and boundary conditions, to examine the medication delivery and its dissemination (diffusion) to organic tissues from multi-layered capsules/tablets and other medication conveyance devices, separately, taken orally or by other conveyance courses. The created models are comprehended utilizing the variational finite element technique, followed by fundamental matrix method, to examine the medication delivery and dissemination, all the more productively. The all inclusive statement of this work is one of the curiosities, which will permit the reenactment of the delivery from a wide scope of cases/tablets and medication conveyance devices, outlining a wide range of utilizations. The fundamental point of this work is to help in a superior comprehension of the delivery component and dissemination from the drug delivery devices utilizing the models, which thus will be useful to decrease the endeavors and expenses of creating and planning new improved conveyance devices. The reproductions acquired, are contrasted with the experimental information to demonstrate the attainability and viability of the introduced work.

#### Non-polynomial models in theory of Bose-Einstein condensates

Konstantin Zloshchastiev1

1Durban University of Technology, Institute of Systems Science, South Africa

###### Abstract

Models of Bose-Einstein condensates based on quantum wave equations with polynomial nonlinearity with respect to wave function were historically first to appear. Those models, such as the Gross-Pitaevskii (cubic Schrodinger) equations, were motivated by perturbation theory while disregarding certain vacuum effects and nonlocality. More recently, various nonperturbative arguments suggested that nonpolynomial nonlinearities, such as logarithmic, should occur in condensate equations in order to account for missed effects properly. Here, a comparative study is done of the propagation of sound pulses in elongated Bose-Einstein condensates in Gross-Pitaevskii and logarithmic models, by means of the Thomas-Fermi approximation. It is shown that in the linear regime the propagation of small density fluctuations is essentially one-dimensional in both models, in the direction perpendicular to the cross section of a condensate lump. Under these approximations, it is shown that speed of sound scales as a square root of particle density in the case of the Gross-Pitaevskii condensate, but it is constant in a case of the homogeneous logarithmic condensate.

#### On the satellite attitude determination using simple environmental models and sensor data

Angel Porras-Hermoso1 , Javier Cubas2 , Santiago Pindado3

1Instituto Universitario de Mircrogravedad "Ignacio Da Riva" (IDR/UPM), ETSI Aeronáutica y del Espacio, Universidad Politécnica de Madrid, , Spain
2Instituto Universitario de Mircrogravedad "Ignacio Da Riva" (IDR/UPM), ETSI Aeronáutica y del Espacio, Universidad Politécnica de Madrid, , Spain
3Instituto Universitario de Mircrogravedad "Ignacio Da Riva" (IDR/UPM), ETSI Aeronáutica y del Espacio, Universidad Politécnica de Madrid, , Spain

###### Abstract

Attitude determination represents a fundamental task for most of the spacecrafts. This task relies fundamentally on three aspects: the selection of sensors, the estimation of relevant environmental conditions and the algorithms that relate the sensor measurements to expected conditions in the reference frame. Each one of these aspects has an impact on the accuracy that the system can achieve. However, two factors stand out above the others in terms of accuracy: the sensor quality (calibration, range, etc), and the precision of the environmental models. The computation of the satellite attitude needs at least of two independent measurements (magnetometers, solar sensors…), whit their corresponding simulated measurement in the reference frame. However, the number of measurements can be reduced to one if the satellite attitude is constrained. This paper discusses the process to calculate the satellite attitude and the main environmental models used (Earth magnetic model, Sun position model, Albedo model) including orbit propagation. In addition, this methodology can be extended to measure the performance of a sensor if the satellite attitude can be derived from the other measurements and satellite constrains. The methodology is checked with the data from the UPMSat-2 mission. This is a 50-kg satellite developed at the Technical University of Madrid that was launched in September 2020.

#### Structural Stability and Electron Density Analysis of Doped Antimonene: A First-Principles Study

Arash Yazdanpanah1

1Shahid Beheshti University, Electrical Engineering, Iran, Islamic Republic Of

###### Abstract

— In this paper, the stability, electronic, and magnetic properties of doped antimonene were investigated using a first-principles Study. The thermodynamic parameters such as cohesive energy, binding energy, and charge transfer demonstrate that the doped structures are stable. The results of the band structure and the density of state indicate that the structure with group IV dopant is a p-type semiconductor, while the structure with group V is intrinsic and for group VI behaviors as n-type semiconductor. P-orbital of dopants and neighbor Sb atoms are the largest contribution to the magnetic moment changes near the Fermi level. For Si and S impurity atoms, the effective mass of structure for conduction band is more than for valence band, which shows that in these structures the carrier mobility of holes is more than electrons, while for p dopant the effective mass of valence band is more than the conduction band.

#### Understanding the outbreak of COVID-19 in Ecuador

Cristian Vacacela Gomez1

1Yachay Tech University , School of Physical Sciences and Nanotechnology, Ecuador

###### Abstract

This study presents a mathematical approach that can be used to estimate the variability of the growth rate coefficient (λ), the total number of cases and the midpoint of maximum infection due to COVID-19 pandemic. The different parameters are quantified using one-year data set reported for Ecuador (from March 2020 to February 2021) and the (discrete or differential) logistic model. In particular, the results evidence that the most critical months of the pandemic in Ecuador were March and April 2020 with a λ> 0.2 day-1. In the following months the outbreak continues with low growth rate values (λ< 0.02 day-1) but in a variable way, which can be attributed to state health policies and social behaviours of the population. The estimated number of confirmed cases around 409 K agrees with the data reported at the end of May 2021, validating the proposed mathematical approach. Furthermore, this approach can be used to study the effect of COVID-19 and predicts its consequences in another countries, allowing to revenue new decisions against the COVID-19 disease.

###### Acknowledgements:

T.T. and C.V.G thanks Universidad Técnica Particular de Loja for supporting the present work.

#### A general method for rotational averages

Reed Nessler1 , Tuguldur Begzjav2

1Texas A&M University, Department of Physics and Astronomy, United States
2National University of Mongolia, Department of Physics, Mongolia

###### Abstract

The theory of nonlinear spectroscopy on randomly oriented molecules leads to the problem of averaging molecular quantities over random rotation. We solve this problem for arbitrary tensor rank by deriving a closed-form expression for the rotationally invariant tensor of averaged direction cosine products. From it, we obtain some useful new facts about this tensor. Our results serve to speed the inherently lengthy calculations of nonlinear optics.

###### Acknowledgements:

We wish to acknowledge G. Agarwal for useful discussions. We acknowledge the support of Office of Naval Research Award No. N00014-16-1-3054 and Robert A. Welch Foundation Grant No. A-1261. The research has also received funding from the National University of Mongolia under grant agreement P2020-3967

#### Solving partial differential equations in deformed grids by estimating local average gradients with planes

Aarne Pohjonen1

1University of Oulu, Materials and Mechanical Engineering, Faculty of Technology, Finland

###### Abstract

For constructing physical science based models in irregular numerical grids, an easy-to-implement method for solving partial differential equations has been developed, and its accuracy has been evaluated by comparison to analytical solutions that are available for simple initial and boundary conditions. The model is based on approximating the local average gradients of a field by fitting equation of plane to the field quantities at neighbouring grid positions and then calculating an estimate for the local average gradient from the plane equations. The results, comparison to analytical solutions, and accuracy are presented for 2 dimensional cases.

###### Acknowledgements:

The funding of this research activity under the auspices of Genome of Steel (Profi3) project through grant #311934 by the Academy of Finland is gratefully acknowledged.

#### Experimental validation of mean pitch theory

Tomasz Meda1 , Andrzej Rogala2

1Military Institute of Armament Technology, Mazowieckie, Poland
2Military Institute of Armament Technology, , Poland

###### Abstract

There are several types of exterior ballistic models used to calculate projectiles flight trajectories. The most complex 6 degree of freedom rigid body model has many disadvantages for use it to create firing tables or rapid calculations in fire control systems. Some of ballistic phenomena can be simplified by empirical equations without significant loss of accuracy. This approach allowed to create standard NATO ballistic model for spin stabilized projectiles named Modified Point of Mass Model. For fin (aerodynamically) stabilized projectiles like mortar projectiles simple Point of Mass Model is commonly used. The PM Model excludes many flight phenomena in calculations. In this paper authors show the mean pitch theory as an approximation of the natural fin stabilised projectile pitch during flight. The theory allows for simple improvement of accuracy of the trajectories calculation. To validate the theory data obtained from shooting of supersonic mortar projectiles were used. The comparison of accuracy between simple PM Model and PM Model including mean pitch theory were shown. Results were also compared with the angle of response theory.

#### A Method of Determining the Parameters in systems with serialized Current-Voltage Characteristics

Richard Ocaya1

1University of the Free State, Physics, South Africa

###### Abstract

We propose a method of determining the parameters of systems with serialized characteristics, which may suggest the existence of symmetry in the system. The method is demonstrated in extracting the parameters of a metal-semiconductor in the presence of significant series resistance, which is itself important but limits the accuracy of the existing methods in the determination of the other calculated parameters such as barrier height and ideality factor. We show the steps involved in establishing whether symmetry exists, and show that some functional interrelations between the parameters and the independent variables can readily be established. We use actual measurement data from an experimental diode and show that the results outperform the popular Cheung-Cheung approach. This general approach, therefore, represents a significant advancement in the analysis of serialized empirical data.

#### Nonexistence of global solutions for damped abstract wave equations with memory

Jorge Esquivel-Avila1

1Universidad Autónoma Metropolitana, Ciencias Básicas, Mexico

###### Abstract

We analyze the nonexistence of global solutions for a class of abstract nonlinear wave equations with memory and linear dissipation. Recently, several articles have consider this problem for viscoelastic wave, Kirchhoff and Petrovsky equations with arbitrary positive values of the initial energy. In order to cover several wave-type equations we consider an abstract formulation and improve previous results.

###### Acknowledgements:

This work was supported by CONACYT under grant 684340, and by the Universidad Aut\'onoma Metropolitana.

#### Network analysis of nanoscale energy conversion processes

Mario Einax1

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

###### Abstract

Nanoscale energy conversion processes are studied in the framework of state-space models. An elegant network representation of the underlying master equation can be used to describe the dynamics by a graph comprising states and transitions between them represented by nodes and links, respectively. The network analysis is motivated by the search for some generic features of nonequilibrium steady states. Particular segments of this network represent input (driving) and output processes that provide a way to introduce a coupling to several heat reservoirs. In addition, the network representation scheme allows one to decompose the stationary dynamics as cycles. The cycle analysis is a convenient tool for analyse models of machine operations, which are characterized by different nanoscale energy conversion processes. By introducing the cycle affinity, we are able to calculate the zero-current limit. Both the maximum achievable efficiency and the open-circuit voltage of the systems with different heat reservoirs are obtained in the zero-affinity limit.

###### Acknowledgements:

M.E. gratefully acknowledges funding by a Research Initiation Grant at BIUST.

#### Beyond the brain : towards a Mathematical Modeling of Emotions

Benjamin ambrosio1

1Le Havre Normandie University, Mathematics, France

###### Abstract

The aim of this talk is to describe a mathematical approach to characterize the emergence of emotional fluxes in the human psyche. Going beyond classical pscychological approaches, our model relies on the idea that emotions can be better described by analogy with electromagnetic waves. In this setting, specific emotions correspond to specific frequencies and our psychic state results from the summation of different caracteristic frequencies. Our model of psychic state is a dynamical system whose evolution results from interactions between external inputs and internal reactions. The model provides both qualitative (frequencies) and quantitative (intensity) components. It aims to be applied to real life situations (in particular in work environments) and we will provide a typical example which naturally leads to a problem of control.

#### Paths of Zeros in Analytic Representation of Finite Quantum Systems Employ Different Species of matrices

Hend Eissa 1

1Electronic technology college , Computing and information technology , Libyan Arab Jamahiriya

###### Abstract

A quantum systems in $\mathscr{D}$ -dimensional Hilbert space Employ arithmetic technology. We concentrate on a set analytic representation in a cell $\mathfrak{S}$ which represents the finite quantum system. The time evolution of the system produces $d$ paths of zeros. The main concept is to confine, our attention, to matrices such as: Swap matrix and vandemonde matrix get in matrix form instead periodic Hamiltonian matrix.The real power of the Displacement operator $\mathfrak{T}$, has periodic system as operator evolution time, is described. In numerical models in particular various, which demonstrate these motif,are introduced In this paper.

#### Planets’ perihelion between Newton and Einstein

Christian Corda1

1Istituto Livi, Mathematics and Physics, Italy

###### Abstract

It is shown that, contrary to a longstanding conviction older than 160 years, the advance of Mercury’s perihelion can be achieved in Newtonian gravity with a very high precision by correctly analyzing the situation without neglecting Mercury’s mass. General relativity remains more precise than Newtonian physics, but Newtonian framework is more powerful than researchers and astronomers were thinking till now, at least for the case of Mercury. The Newtonian formula of the advance of planets’ perihelion breaks down for the other planets. The predicted Newtonian result is indeed too large for Venus and Earth. Therefore, it is also shown that corrections due to gravitational and rotational time dilation, in an intermediate framework which analyzes gravity between Newton and Einstein, solve the problem. By adding such corrections, a result consistent with the one of general relativity is indeed obtained. Thus, the most important results of this Lecture are two: (i) It is not correct that Newtonian theory cannot predict the anomalous rate of precession of the perihelion of planets’ orbit. The real problem is instead that a pure Newtonian prediction is too large. (ii) Perihelion’s precession can be achieved with the same precision of general relativity by extending Newtonian gravity through the inclusion of gravitational and rotational time dilation effects. This second result is in agreement with a couple of recent and interesting papers of Hansen, Hartong and Obers. Differently from such papers, in the present Lecture the importance of rotational time dilation is also highlighted. Finally, it is important to stress that a better understanding of gravitational effects in an intermediate framework between Newtonian theory and general relativity, which is one of the goals of this Lecture, could, in principle, be crucial for a subsequent better understanding of the famous Dark Matter and Dark Energy problems. This Lecture is founded on the research paper C. Corda, "The secret of planets’ perihelion between Newton and Einstein", Physics of the Dark Universe 32 (2021) 100834.

#### Predictive modeling on the example of a gas turbine plant

Eugenia Echkina1 , Valentin Lvov2

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

###### Abstract

The ability to accurately predict the operation of a particular mechanism and, on the basis of this, estimate the equipment life is a very important task. The amount of losses of the enterprise can depend on such study, as well as the health of many people whose lives depend on the health of the working installation. As part of this work, the main time series models were considered and the most suitable for the study was selected. The operation of a gas turbine plant was studied and a forecast was made. On the basis of the study, linear regression, ARIMA and moving average models were built and evaluated.

###### Acknowledgements:

The study was carried out jointly with BMSsoft d.o.o Company.

#### Problems of increasing the efficiency of using fixed and working capital of petrochemical enterprises

Gulnaz Galeeva1

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

###### Abstract

The article discusses topical issues of analysis of the state and improving the quality of management of the structure of fixed and working capital of enterprises of the petrochemical complex. Evaluation of indicators affecting the efficiency of their use made it possible to determine the directions for improving the process of forming the value of fixed and circulating assets of petrochemical enterprises. In conclusion, the authors highlight the successful practices of enterprise asset management.

#### String Topological Robotics 2

My Ismail Mamouni1

1CRMEF Rabat, Mathematics, Morocco

###### Abstract

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

#### EFFICIENT NUMERICAL METHOD FOR SOLVING ADVECTION-DIFFUSION-REACTION PROBLEMS ON A SPHERE

Yuri Skiba1

1Universidad Nacional Autónoma de México (UNAM), Centro de Ciencias de la Atmósfera (Centre for Atmospheric Sciences), Mexico

###### Acknowledgements:

The authors are grateful to the National Research System of Mexico (SNI, CONACYT) for scholarships in research and education.

#### Dark Matter in the Standard Model Extension in Non-commutative Geometry (NCG)

BERKANE Amina1

1University of M'Sila, Algeria, Laboratory of Physics and Chemistry of Materials, Department of Physics, Algeria

###### Abstract

It is for the most part expected that dark matter is important to clarify the rotation of the galaxy, it has effectively been seen that the non-commutative geometry background can achieve this objective similarly. The purpose of this paper is to investigate a relationship between non-commutative geometry, a certain aspect of dark matter. We are based on a simple mathematical argument that shows that the appearance of dark matter with respect to flat rotation curves in galaxies and galaxy clusters is also a consequence of non commutative geometry.

#### Human machine interface (HMI) based on a multi-agent system in a water purification plant.

Eduardo Mendoza Merchán1 , Samuel Alvear Celi2 , Joselyne Andramuño Cando 3 , José Núñez Álvarez4

4Universidad de la Costa, Energy Department, Colombia

###### Abstract

The applications of multi-agent systems (MAS) are growing increasingly in the industrial field due to the advantages inherent to their characteristics and properties, the use of distributed automation architectures, which have satisfactorily solved control problems that its complexity and dynamic behavior have not been properly resolved with other approaches under these conditions, intelligent agents must meet the requirements of current automation systems, such as autonomy, flexibility, reconfiguration, in concurrent and collaborative systems, which traditionally do not have been designed to satisfy these characteristics. In the present work, a distributed architecture is proposed for the design of an intelligent agent in a Human-Machine Interface (HMI) for the supervision of the filtering stage of a water purification plant, characterized by the ability to collaborate with the other agents that make up the entire plant. For the projection and design of the system, the Unified Modeling Language (UML) and Petri nets (PN) are used for the simulation and validation of the system, and the implementation of the agent from macros in C language, starting from a methodology of multi-agent design that is applied in this document. The implementation of the intelligent agent in an HMI associated with multi-agent architecture, which allowed to evaluate its behavior through the analysis of the properties of the PN and experimental tests, demonstrating the correct operation of the device, response times and its dynamic behavior based on of the functional requirements of the water purification plant and comparisons with similar works.

###### Acknowledgements:

Thanks to the Universidad Católica de Santiago de Guayaquil, for its support in research projects

#### Physics-Guided Kinetic Energy Density Expansion: A Scaling Analysis

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

###### Abstract

An approach guided by physical consistency in determining the general forms of D-dimensional kinetic energy density functionals (KEDF) has been demonstrated previously [Int. J. Quantum Chem. 117, e25373, 2017], producing an expansion which contains the majority of the known one-point KEDF forms. It is known that any noninteracting KEDF shall necessarily have a homogeneity degree of 2 in coordinate scaling. This paper demonstrates that this condition is already satisfied in the general expansion despite not being conceived with the scaling as a constraint. Furthermore, other constraints on the KEDF form are also established with the goal of analyzing its general properties.

#### A general one-dimensional traffic model for motion of molecular motors on microtubules of variable length

Emma Aldrich1 , Beth Reed2 , Laurentiu Stoleriu3 , Dan Mazilu4 , Irina Mazilu5

1Washington and Lee University , Physics and Engineering , United States
2Washington and Lee Univeristy, Physics and Engineering , United States
3"Al. I. Cuza" University , Physics, Romania
4Washington and Lee University, Physics and Engineering, United States
5Washington and Lee University, Physics and Engineering, United States

###### Abstract

We present a traffic model inspired by the motion of molecular motors along microtubules, represented by particles moving along a one-dimensional track of variable length. As the particles move unidirectionally along the track, several processes can occur: particles already on the track can move to the next open site, additional particles can attach at unoccupied sites, or particles on the track can detach. We study the model using mean-field theory and Monte Carlo simulations, with a focus on the steady-state properties and the time evolution of the particle density and particle currents. For a specific range of parameters, the model captures the microtubule instability observed experimentally and reported in the literature. This model is versatile and can be modified to represent traffic in a variety of biological systems.

#### A one-dimensional modified TASEP model on a track of variable length: analytical and computational results

Beth Reed1 , Emma Aldrich2 , Laurentiu Stoleriu3 , Dan Mazilu4 , Irina Mazilu5

1Washington and Lee Univeristy, Physics and Engineering , United States
2Washington and Lee University , Physics and Engineering , United States
3"Al. I. Cuza" University , Physics, Romania
4Washington and Lee University, Physics and Engineering, United States
5Washington and Lee University, Physics and Engineering, United States

###### Abstract

We present analytical solutions and Monte Carlo simulation results for a one-dimensional modified TASEP model inspired by the interplay between molecular motors and their cellular tracks of variable lengths, known as microtubules. Our TASEP model incorporates rules for changes in the length of the track based on the occupation of the first two sites on the track. Using mean-field theory, we derive analytical results for the particle densities and particle currents and compare them with Monte Carlo simulations. These results show the limited range of mean-field methods for models with localized high correlation between particles. The variability in length adds to the complexity of the model, leading to emergent features for the evolution of particle densities and particle currents compared to the traditional TASEP model.

#### Intelligent multi-agent architecture for a supervisor of a water treatment plant.

Eduardo Mendoza Merchán1 , Joselyne Andramuño Cando 2 , José Núñez Álvarez3 , Luis Córdova Rivadeneira4

3Universidad de la Costa, Energy Department, Colombia

###### Abstract

The rapid development of Information and Communication Technologies (ICT) and high-capacity hardware components make it necessary to achieve a strong integration of automatic systems based on new paradigms on intelligent distributed architectures, where require highly complex supervision and control tasks, due to the generated requirements of the new production systems, the high number of variables to control and the advancement of technologies, especially in industries where continuous processes have been established. In the present work, a distributed hierarchical modular architecture is proposed for a supervision system, based on multi-agent systems (MAS), oriented to the management of processes in the filtration stage of a water purification plant, using a methodology to the implementation of intelligent agents that allow to project, design, verify and validate the system. This methodology is fundamentally based on the use of the Unified Modeling Language (UML) for its projection and Petri nets (PN) for the simulation and validation of properties, which allows to guarantee the modularity, flexibility, and robustness of the proposed system. The architectures of the intelligent agents in the different programmable devices are modeled and simulated to achieve an adequate interaction and collaboration, allowing to reduce the conflicts that may be generated between them. The evaluation of the distributed architecture focuses on the fulfillment of the functional requirements and evaluation metrics, which, through the analysis of the properties of the Petri net, allows to determine the correct operation of the system and its dynamic behavior in the face of unforeseen situations at different levels of automation.

###### Acknowledgements:

Thanks to the Universidad Católica de Santiago de Guayaquil, for its support in research projects

#### Stochastic SEAIHRD model of epidemic propagation

Simon Serovajsky1

1al-Farabi Kazakh National University, Mathematics, Kazakhstan

###### Abstract

А compartmental model in epidemiology is considered. The whole population here is divided into compartments susceptible, exposed, asymptomatic, mildly ill, hospitalized, recovered, died. It is assumed that susceptible can pass into exposed compartment, becoming infected from asymptomatic and mildly ill. Exposed people can become ill in any form or not at all. Patients in any form either recover or their illness becomes more severe. Hospitalized people can die. All those who have recovered acquire immunity. The corresponding deterministic model is a system of nonlinear differential equations. In the stochastic case, each transition from one compartment to another is considered as a random event. A differential-difference equation is derived for the probability of finding a population in a certain state.

#### Investigation of heat transfer in metal nanofilms irradiated with ultrashort laser pulses: two-temperature model

Galina Mikheeva1 , Alexei Pashin2 , Igor Kudinov3

1Samara State Technical University, Department "Theoretical Foundations of Heat Engineering and Hydromechanics", Russian Federation
2Samara State Technical University, Department "Theoretical Foundations of Heat Engineering and Hydromechanics", Russian Federation
3Samara State Technical University, Department "Theoretical Foundations of Heat Engineering and Hydromechanics", Russian Federation

###### Abstract

A numerical study of heat transfer between an electron gas and a crystal lattice in a metal nanofilm under irradiation with an ultrashort laser pulse was carried out on the basis of a parabolic two-temperature model of thermal conductivity presented in a dimensionless form. For the numerical solution, the finite difference method was used using the explicit-implicit Crank-Nicholson scheme. As a result of the numerical study, it was found that with an increase in the thickness of the plate, the equilibrium temperature decreases, and the time for the onset of thermal equilibrium between the electrons and the crystal lattice increases.

###### Acknowledgements:

The reported study was funded by RFBR, project number 20-38-70021

#### A Generalized Pattern Search Algorithm Methodology for solving an Under-Determined System of Equality Constraints to achieve Power System Observability using Synchrophasors

1Effat University , College of Engineering, Saudi Arabia

###### Acknowledgements:

This study is supported financially by The Specific Fund Account of National Technical University of Athens (http://edeil.ntua.gr/) project no. 11444. The authors thank the specific account research for supporting the project.

#### Analysis of the error distribution density convergence with its orthogonal decomposition in navigation measurements

Igor Vorokhobin1 , Iryna Zhuravska2 , Igor Burmaka3 , Inessa Kulakovska4

1National University “Odessa Maritime Academy”, Educational and Scientific Institute Marine Transportation and Technologies, Ukraine
2Petro Mohyla Black Sea National University, Faculty of Computer Science, Ukraine
3National University “Odessa Maritime Academy”, Educational and Scientific Institute Marine Transportation and Technologies, Ukraine
4Petro Mohyla Black Sea National University, Faculty of Computer Science, Ukraine

###### Abstract

For the analysis of statistical materials of the accuracy of determining the location of a moving object, the Gaussian normal distribution is usually used. However, if the histogram of the sample has “heavier tails”, the determination of latitude and longitude's error according to Gaussian function is not correct and requires an alternative approach. To describe the random errors of navigation measurements, mixed laws of a probability distribution of two types can be used: the first type is the generalized Cauchy distribution, the second type is the Pearson distribution, type VII. In this paper, we analyze the convergence of the distribution density of a mixed law of the first type with its orthogonal decomposition depending on the number of terms. In this distribution, the significant parameter n is responsible for the heaviness of the tail. Moreover, events moving beyond three standard deviations occur several orders of magnitude more often than with a normal distribution. When considering the navigation of moving objects (on the sea, air, land, etc.), such heavy tails take into account the possibility of critical situations (collisions of objects in overcrowded conditions or going beyond the cramped traffic corridor), and they cannot be neglected. It is advisable to use mixed distribution functions, in particular, when observations are stopped at some point. This can be in the absence of a signal from terrestrial or satellite radio navigation systems, as well as when it enters the zone of high electromagnetic radiation or electronic warfare equipment (signal jammers). In this case, the determination of the location of a moving object (observation) is carried out using visual observations of fixed external landmarks with known coordinates. This leads to a significant increase in the measurement errors of the navigation parameters of a moving object (ship, aircraft, vehicle, etc.). With the specified shortage of statistical materials, it is not possible to use the standard procedure to determine the distribution law of random variables, according to which the random components of the navigation measurement error are distributed. However, the central moments of the distribution can be estimated. It is shown in the work that if the histogram of the sample has “heavy tails”, then it is possible to use the expansion of the error distribution density using orthogonal Hermite polynomials, without having its analytical expression. In the process, the best convergence of the density with its orthogonal decomposition is achieved when it contains only one term. Our numerical results show that the approximation of the distribution function using the Gram-Charlier series of type A makes it possible to apply the orthogonal decomposition to describe the density of errors in navigation measurements. To compare the curves of density and its orthogonal decomposition, the values were calculated, and the results are presented in graphical form. The research results showed that the normalized density and its orthogonal decomposition practically coincide.

#### The Extension of the Physical and Stochastic Problems to Space-Time-Fractional Differential Equations

E. A. Abdel-Rehim1

1Suez Canal University, Faculty of Science, Mathematics, Egypt

###### Abstract

The fractional calculus gains wide applications nowadays in all fields. The implementation of the fractional differential operators on the partial differential equations make it more reality. The solutions of the space-time-fractional differential equations modelling physical, biological, medical, etc., explain the real life problems than the classical partial differential equations. Some new published papers on this field made many treatments and approximations to the fractional differential operators making them loose their physical and mathematical meanings. In this paper, I answer the question: why do we need the fractional operators?. I give brief notes on some important fractional differential operators and their Gruenwald-Letnikov schemes. I implement the Caputo time fractional operator and the Ritz-Feller operator on some physical and stochastic problems. I give some numerical results to some physical models to show the efficiency of the Gruenwald-Letnikov scheme and its shifted formulae.

#### Lower bound for the spectral radius of the starlike trees

Rubí Arrizaga-Zercovich1

1Universidad Santiago de Chile, Departamento de Matemática y Ciencias de la Computación, Chile

###### Abstract

A tree is a connected acyclic graph. A tree is called a starlike if exactly one of its vertices has degree greater than two. Let $\lambda _{1}$ be the largest eigenvalue of the adjacency matrix of a starlike tree. In this work, we obtain a lower bound for the spectral radius of a starlike tree. This bound only depends of the maximum degree of the vertices.

#### Upper bound for the energy of the starlike trees

Rubí Arrizaga-Zercovich1 , Luis Medina2

1Universidad Santiago de Chile, Departamento de Matemática y Ciencias de la Computación, Chile
2Universidad de Antofagasta, Departamento de Matemáticas, Chile

###### Abstract

The energy graph was defined by Gutman, in 1978, as the sum of the absolute values of the eigenvalues of the adjacency matrix. In this work, we obtain a upper bound for the energy of a starlike tree. This bound is obtained in function of the number of vertices and the maximum degree of the vertices.

#### A set of application models for stochastic mixed-integer second-order cone optimization

1University of Jordan, mathematics, Jordan
2University of Jordan, mathematics, Jordan

###### Abstract

Second-order cone programming problems are a class of convex optimization problems and there are known polynomial algorithms for solving them. Stochastic second-order cone programming problems have also been studied since the 1990s as a tool for handling uncertainty in data. A new class of interest to the optimization community is the mixed-integer version of these problems that requires some variables are restricted to be an integer. Since mixed-integer programs are generally known to be NP-hard, bringing applications to the surface can detect tractable special cases and inspire for further algorithmic improvements in the future. In this talk, we describe six application models leading to stochastic mixed-integer second-order cone programming problems. Namely, we describe a stochastic discrete facility location problem, a portfolio optimization problem with CVaR and diversification constraints, an inventory management problem, a routing problem based on battery swap station, a stochastic discrete Steiner tree problem, and a capital budgeting problem.

#### Quantum Vacuum Gravitation. Matter-Antimatter Antigravity.

Constantin Meis1

1CEA - Saclay, National Institute for Nuclear Science and Technology, France

###### Abstract

Without stating any assumptions or making postulates we show that the electromagnetic quantum vacuum, which derives directly from Maxwell’s theory, plays a primary role in quantum electrodynamics, particle physics, gravitation and cosmology. Photons are local oscillations of the electromagnetic quantum vacuum field guided by a non-local vector potential wave function. The electron-positron elementary charge derives naturally from the vacuum field and is related to the photon vector potential. We establish the masse-charge equivalence relation showing that the masses of all particles (leptons, mesons, baryons) and antiparticles have electromagnetic origin. In addition, we deduce that the gravitational constant G is an intrinsic property of the electromagnetic quantum vacuum putting in evidence the electromagnetic nature of gravity. We show that Newton’s gravitational law is equivalent to Coulomb’s electrostatic law. Furthermore, we draw that G is the same for matter and antimatter but gravitational forces are repulsive between particles and antiparticles because their masses bear naturally opposite signs. The electromagnetic quantum vacuum field could be the natural link between particle physics, quantum electrodynamics, gravitation and cosmology constituting a basic step towards a unified field theory.

#### Mathematical modelling of optical radiation transport in biological tissues under the conditions of moveable integrating spheres registration

Tatiana Karpova1 , Nikita Kovalenko2 , Georgii Aloian3 , Oleg Ryabushkin4

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

###### Abstract

To describe the propagation of radiation in biological tissue, it is crucial to know the tissue's optical characteristics. Integrating spheres method is widely used for experimental determination of optical properties of biological tissues. In this method, radiation scattered by the test sample in forward and backward directions is detected by the integrating spheres, along with the radiation that passed through the sample without scattering. In order to increase information content of the measurements, a moveable integrating spheres method was proposed, allowing one to register scattered radiation at different distances from sample surface to sphere ports. In this work, using the multilayer Monte Carlo method a numerical simulation of radiation propagation in a turbid medium was carried out under the conditions of detecting scattered radiation by moveable and stationary integrating spheres. Random errors were added to the direct problem solution in order to simulate experimental inaccuracies. The corresponding inverse problems were solved and the errors arising in the determination of optical properties (albedo, scattering anisotropy, optical depth) were compared in the cases of moveable and fixed spheres. It is shown that the same error in the inverse problem input data leads to smaller root-mean-square deviation from the true values when reconstructing albedo and anisotropy with the moveable spheres method, compared to the classical stationary spheres approach.

#### Nonlinear dynamics for the 3D ideal gas flow over the cylinder

Nikolay Evstigneev1 , Oleg Ryabkov2

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

###### Abstract

The system of compressible gas is considered in the 3D bounded domain with the inflow and outflow boundary conditions. The cylinder is located in the domain. Such problem is simulated using the high order WENO-scheme for inviscid part of the equations and using Pade approximation for the viscous tensor part with the forth order temporal discretization. The method of Proper Orthogonal Decomposition (POD) is applied to the problem at hand in order to extract the most active nodes. Cascades of bifurcations of periodic orbits is found that correspond to the excitation in different POD modes.

###### Acknowledgements:

The study was supported by the Russian Foundation for Basic Research (grants No. 18-29-10008mk and No. 20-07-00066a)

#### Disconnected stationary solutions for 3D Kolmogorov flow problem: preliminary results

Nikolay Evstigneev1

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

###### Abstract

The extension of the classical A.N. Kolmogorov's flow problem for the stationary 3D Navier-Stokes equations on a stretched torus for velocity vector function $\mathbf{u}:\mathbb{T}(\alpha)^3 \to \mathbb{R}^3$ and pressure scalar function $p:\mathbb{T}(\alpha)^3 \to \mathbb{R}$ is considered as: $$(\mathbf{u}, \nabla) \mathbf{u} + \nabla p - \frac{1}{R}\bigtriangleup \mathbf{u} = (\sin(\beta y);0;0)^\mathrm{T},$$ $$\nabla \cdot \mathbf{u} = 0,$$ where $R$ is the Reynolds number (bifurcation parameter), $\alpha$ is the stretch factor for the domain $\mathbb{T}(\alpha)^2:=[0;2\pi/\alpha] \times [0;2\pi] \times [0;2\pi]$ and $\bigtriangleup$ is the Laplace operator. The force vector field depends only on the second spatial variable $y$ and coefficient $\beta$ is an integer. The problem has a trivial solution $u\mathbf{u}=\frac{R}{\beta^2} (\sin(\beta y),0,0)^T$. 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 $(512/\alpha) \times (256)\times(256)$ Fourier harmonics), construction of the solution curves in the parameter-phase space and analysis of disconnected solutions. The system of equations is transformed to the problem $F(\hat{\mathbf{u}}, R) = \mathbf{0}$ for the fixed values of $\alpha=1/2$ and $\beta = 1$ with $R \in [0;11]$. The nontrivial solution curve $\hat{\mathbf{u}}(R)$ that bifurcated from the trivial solution $\hat{\mathbf{u}}_0(R)$ at point $R_0$ is called connected solution curve and $\hat{\mathbf{u}}(R_0) = \hat{\mathbf{u}}_0(R_0)$ at the bifurcation curve. All other curves that bifurcated from the connected curve are also called connected solution curves. Note, that the stability of these solutions is irrelevant and the connected curves are applicable to both subcritical and supercritical bifurcations. The disconnected solution curve $\hat{\mathbf{u}}_d(R)$ is such a solution curve that $\hat{\mathbf{u}}_d,R \neq \hat{\mathbf{u}},R$ for any admissible value of $R$, where $\hat{\mathbf{u}}$ is a connected curve. The paper presents bifurcation diagrams and shows the location of such disconnected curves. At least one disconnected curve is found that shares stability with the main curve in the parameter space. Such curves can be responsible for the multistability and explain the nonlinear stability loss.

###### Acknowledgements:

The study was supported by the Russian Foundation for Basic Research (grants No. 18-29-10008mk and No. 20-07-00066a)

#### A new approximate deconvolution subgrid model for LES: application to two-dimensional turbulence

Andrzej Boguslawski1 , Karol Wawrzak2 , Agata Paluszewska3 , Bernard Geurts4

1Czestochowa University of Technology, Department of Thermal Machinery, Poland
2Czestochowa University of Technology, Faculty of Mechanical Engineering and Computer Science, Poland
3Czestochowa University of Technology, Department of Thermal Machinery, Poland
4University of Twente, , Netherlands

###### Abstract

The paper presents a new approximate deconvolution subgrid model for Large Eddy Simulation. The top-hat filter implied by the second-order central finite differences is discretised using the discrete Fourier transform involving all the mesh points in the computational domain. Such a discrete filter kernel is then inverted by the Wiener type inverse filtration. The inverse filter is used to deconvolve the velocity field filtered implicitly by the numerical scheme. Subgrid stresses are calculated directly from the deconvolved velocity field. The model was applied to study the decaying two-dimensional turbulence. The results were compared with the results obtained with the Smagorinsky and the dynamic Germano models. A posteriori testing using the filtered Direct Numerical Simulation obtained with Fourier spectral method is also performed. Although the new model in the version presented applies to periodic problems only, the idea of a high-order discretisation of the filter kernel can readily be extended to more general non-periodic problems.

###### Acknowledgements:

The research was supported by Polish National Science Centre, project no. 2018/29/B/ST8/00262 and by the National Agency for Academic Exchange (NAWA) within the International Academic Partnerships Programme, project ANIMATE no. PPI/APM/2019/1/00062

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

Hafedh Zghidi1 , Maksym Walczak2 , Tomasz Blachowicz3 , Adam Duszenko4

1Silesian University of Technology, Informatics, Poland
2Silesian University of Technology, , Poland
3Silesian University of Technology, Division of Applied Physics, Poland
4Silesian University of Technology, Informatics, Poland

###### Abstract

The article presents a complete solution for filtering and diffusive fractal characterization of 2-dimensional images. This includes preparing the sample by subtracting background, application of random walk procedure and its parallelization using two different approaches. For each technique the processing time is measured to compare speedups with regard to a sequential implementation. To prove the correctness of the results, a black square is used as the reference sample, for which diffusive fractal dimension is known and equls 2. Finally the results for a complex image are elaborated.

#### Review on de Bruijn shapes in one, two and three dimensions

Pedro Juan Roig1

1Miguel Hernández University , Department of Computing Engineering, Spain

###### Abstract

Working with ever growing datasets may be a time consuming and resource exhausting task. In order to try and process the corresponding items within those datasets in an optimal way, de Bruijn sequences may be an interesting options due to their special characteristics. Such sequences are unidimensional, although the same principle may be extended to involve more dimensions, such as de Bruijn tori for bidimensional patterns, or de Bruijn hypertori for three tridimensional patterns, even though those might be further expanded up to infinite dimensions. In this context, the main features of all those de Bruijn shapes are going to be exposed, along with some particular instances, which may be useful in pattern location in one, two and three dimensions.

#### Supercomputer power consumption predictions using machine learning, nonlinear algorithms, and statistical methods

Jiří Tomčala1

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

###### Abstract

This paper describes various methods for predicting time series produced by complex systems. It illustrates the differences between machine learning methods, nonlinear algorithms, and statistical methods in their approach to prediction, and tries to explain in depth the principles of some of the most widely used representatives of these types of prediction methods. All of these methods are then tested on a time series from the real world: the course of power consumption of a supercomputer infrastructure. The reader is gradually acquainted with data analysis, preprocessing, the principle of the methods, and finally with the prediction itself. The main benefit of the work is the final comparison of the results of this testing in terms of the accuracy of the predictions, and the time needed to calculate them.

###### Acknowledgements:

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

#### The correlation analysis of the daily Covid-19 new cases data series in Albania.

Agron Gjana1 , Sandër Kovaçi2

1Polytechnic University of Tirana, Department of Mathematical Engineerin, Albania
2Polytechnic University of Tirana, Department of Mathematical Engineering, Albania

###### Abstract

Abstract. We analyzed herein the daily new positive covid-19 cases recorded in Albania by using the empirical nonlinear and nonstationary time series approach. We observed that the distribution of the daily new cases is non-stationary and usually has a power law behavior in the low incidence zone, and a bell curve for the remaining part of the incidence interval. We qualified this finding as the indicator intensive dynamics and as proof that up now, the heard immunity has not been reached. By parallelizing the preferential attachment mechanisms responsible for a power law distribution elsewhere in the social graphs, we explain the low daily incidence distribution as result of the imprudent gatherings of peoples. Additionally, the bell-shaped distribution observed for the high daily new cases is agued as outcome of the competition between illness advances and restriction measures. The distribution is acceptably smooth, meaning that the management have been accommodated to the no-surprise days. This behavior is observed also for Greece, and Italy, whereas not for Turkey, Serbia, and North Macedonia, indicating similarities and differences on the management of the pandemic for different countries. Also, we have identified the local presence self-organization properties in different time intervals, but globally there was no apparent unique regime present, and formally we identified two regimes finalized so far, followed by a third one which started in July 2021.

#### EFFICIENT NUMERICAL METHOD FOR SOLVING ADVECTION-DIFFUSION-REACTION PROBLEMS ON A SPHERE

Yuri Skiba1

1Universidad Nacional Autónoma de México (UNAM), Centro de Ciencias de la Atmósfera (Centre for Atmospheric Sciences), Mexico

###### Abstract

The new algorithm proposed in [1] is applied for solving linear advection-diffusion-reaction problems and nonlinear diffusion problems on a sphere. The velocity field on the sphere is assumed to be non-divergent and known. Discretization of differential problems in space is performed by the finite volume method using the Gauss theorem for each grid cell. For time discretization, the method of symmetrized two-cycle componentwise splitting and the Crank-Nicholson scheme are used. The one-dimensional periodic problems, arising at the stage of splitting in the longitudinal direction, are solved with Sherman-Morrison’s formula and Thomas’s algorithm. The highlight of the method is the use of special bordered matrices for the exact (non-iterative) solving the 1D problems arising at the stage of splitting in the latitudinal direction. The bordering procedure requires a prior determination of the solution at the poles. The resulting linear systems have tridiagonal matrices and are also solved by Thomas’s algorithm. The obtained numerical method has the second order of approximation in space and time. It is implicit and unconditionally stable; in addition, the operator splitting provides a direct (non-iterative) and fast implementation of the resulting schemes, as well as the possibility of using parallel computing. The theoretical results obtained in [1] are confirmed numerically by simulating various linear processes on the sphere (diffusion in a spherical sector, diffusion flux through the pole, advection flux through the pole, dispersion of a pollutant emitted from multiple point sources) and nonlinear diffusion processes (spiral waves, nonlinear temperature waves, HS, LS and S blow-up combustion modes and solutions of the Gray-Scott model). Numerical experiments show a high accuracy and efficiency of the method that correctly describes the processes of advection-diffusion on a sphere (including the processes near the poles and through the poles) and the mass balance of matter in forced and dissipative discrete systems. Moreover, in the absence of external forcing and dissipation, the numerical method conserves both the total mass and the L2-norm of the solution.

###### Acknowledgements:

The authors are grateful to the National Research System of Mexico (SNI, CONACYT) for scholarships in research and education.

#### Finding the global minimum of the objective function in a hybrid control structure to compensate for badly damped vibration

Ryszard Dindorf1

1Kielce University of Technology, Department of Manufacturing Engineering and Metrology, Poland

###### Abstract

The paper deals with finding the global minimum of the objective function in a hybrid control structure to compensate for vibrations. The purpose of the hybrid control structure of the servo-hydraulic actuator (SHA) is to compensate for badly damped vibrations after the application of a spring damping device (SDD). A hybrid control structure was proposed to improve the control precision and mitigate the effects of nonlinearity and vibration of the SHA-SDD system. The practical actual use of SHA for position control of the crusher manipulator boom with a mounted breaker for crushing large (oversized) rocks in the jaw crusher space was considered. The SHA cylinder piston rod is flexibly connected to the inner boom by an SDD. Vibration effects can cause the deterioration of response speed, control accuracy, and stability of the SHA-SDD system. The hybrid control structure includes a feedback controller, a feedforward controller, and an input shaping filter. By applying the Euler backward method to the PID feedback controller for both the integral and derivatives in a given sampling period Ts and modifying the differential term of the low pass filter (HLPF), the transfer function GPID in discrete-time with z-domain was established. The SHA-SDD model was saved as the Hammerstein model with unknown parameters that consist of two parts: a static nonlinear part and a dynamic linear part. The static nonlinear subsystem is approximated by the set polynomial degree and is described by the nonlinear function of the nth-order binding the nonlinear output x(k) to the input u(k). The dynamic linear part is the ARX (Auto-Regressive model with Exogenous inputs) model was applied, which represents the relation of input x(k) to output y(k). The combination of the FIR input shaping filter with the FIR feedforward filter was proposed, whereby the oscillations induced by impulse forces are effectively damped, resulting in better control accuracy. The goal of optimizing the hybrid control structure was to find an FIR feedforward filter coefficient that minimizes the objective function. The objective function leads to a convex optimization problem, which means that the global optimal solution is achievable. The gradient vector of the objective function is given by the partial derivatives to each of the independent variables, the second-order partial derivatives can be represented by a square symmetric matrix called the Hessian matrix. Ultimately, the global minimum is solved for the specified coefficient. The global minimum, control error, and its gradients are calculated from the measurement of input signal u and output signal y. Experimental results show that the hybrid control method proposed in this paper can greatly improve the control precision of the SHA-SDD system excited by cyclic impact force

#### Secondary Faraday waves in microgravity

Elena Labrador Vares1 , Pablo Salgado Sánchez2 , Jeff Porter3 , Valentina Shevtsova4

4Microgravity Research Center, Université Libre de Bruxelles, , Belgium

###### Abstract

Recent microgravity experiments have demonstrated that Faraday waves can arise in a secondary instability over the primary columnar patterns that develop after the frozen wave instability. While some numerical studies have investigated this phenomenon, theoretical analyses are only found in the works of Shevtsova et al. (2016) and Lyubimova et al. (2019). Here, we extend these efforts by analysing the stability of a three-layer system, and derive the critical onset of Faraday waves, which appear via Hopf bifurcation. Numerical simulations --- based on a model that reproduces the frozen wave mode with lowest wavenumber --- are carried out to test this result and to analyse the character of the bifurcation. The predicted Hopf bifurcation is confirmed, which constitutes the first observation of modulated secondary Faraday waves. The abrupt growth of these modulated waves above onset indicates that the primary bifurcation is subcritical and is accompanied by a saddle-node bifurcation of periodic orbits that stabilises the (branch of) unstable solutions created in the subcritical Hopf bifurcation. Further above onset, these modulated waves are destroyed via a saddle-node heteroclinic bifurcation. Results for an N-layer configuration, which represents a more general frozen wave pattern, are also presented and compared with the three-layer case and the existing literature.

#### High-speed camera test of newly developed igniter's charges for artillery munition

Aleksandra Plachá1 , Judyta Recko2

1Military Institute of Armament Technology, Ballistics Department, Poland
2Military Institute of Armament Technology, Ballistcs Department, Poland

###### Abstract

The article presents the results of the high-speed camera test of newly developed igniter’s charges for artillery munition. The test was performed to take a closer look at the ignition process of mixtures, that is to check the time-to-ignition of samples and to assess the presence and quantity of solid igniting particles (if any). Five compositions were tested: Three of them contained the new igniter’s charges developed by the Military Institute of Armament Technology and the other two contained black powder in different granularity classes as a comparison mixture. This article presents the collated test results.

###### Acknowledgements:

Special thanks to PhD Marcin NITA for all his knowledge and commitment.

#### The influence of knot types on rope static tensile strength

Łukasz Rybakiewicz1 , Aleksandra Plachá2 , Piotr Ruliński3

1Military Instute of Armament Technology, Development Department , Poland
2Military Institute of Armament Technology, Ballistics Department, Poland
3Military Institute of Armament Technology, Ballistics Department, Poland

###### Abstract

The choice of material, type of braid and rope parameters are a broad issue of great importance in the designing process. An equally important issue is the proper selection of knot type used for attaching the rope to the other elements of a structure, as this is a critical point accumulating major stresses. Inappropriate tying of a rope may decrease its tensile strength by over 50%; therefore, it is an important issue in terms of structural strength. This article investigates different tying configurations of the same rope and shows the influence of knot types on rope static tensile strength.

#### Nash equilibria in seller-buyer supply chains

João Almeida1

1CeDRI-IPB, Polytechnic Institute of Bragança, Mathematics, Portugal

TBA

#### Cluster analysis in Urban Climate

João Almeida1

1CeDRI-IPB, Polytechnic Institute of Bragança, Mathematics, Portugal

TBW

#### Performance Characterization of Dual-Metal Triple-gate-dielectric (DM_TGD) Tunnel Field Effect Transistor (TFET)

Tan Chun Fui1 , Ajay Singh2 , Lim Way Soong3

1Multimedia University Malaysia, Faculty of Information Science and Technology, Malaysia
2NIIT University, Rajasthan, India, Electronics and Communication Engineering, India
3Multimedia University Malaysia, Faculty of Engineering and Technology, Malaysia

###### Abstract

Since, Dual Metal Gate (DMG) technology alone is not enough to rectify the problem of low ON current and large ambipolar current in the TFET, therefore, a novel TFET structure, known as dual metal triple-gate-dielectric (DM_TGD) TFET, has been proposed. We have combined the dielectric and gate material work function engineering to enhance the performance of the conventional FET. In the proposed structure, the gate region is divided into three dielectric materials: TiO2/Al2O3/SiO2. This approach is chosen because high dielectric material alone near the source cannot improve the performance due to increase in fringing fields. This paper presents the detail processing of the proposed structure. We have evaluated and optimized the dc performance of the proposed N-DM_TGD TFET with the help of 2-D ATLAS simulator. The results were compared with those exhibited by dual metal hetero-gate-dielectric TFET, single metal hetero-gate-dielectric TFET and single metal triple-gate-dielectric TFET of identical dimensions. It has been observed that the DM_TGD device offers better transconductance (gm), lower subthreshold slope, lower ambipolar current and larger ON current.

#### The influence of accidental physical contacts between individuals on viral infection

Igor Derevich1 , Anastasiia Panova2

1Moscow State Technical University by N.E. Bauman (BMSTU), Faculty of Fundamental Sciences, Department of Applied Mathematics, , Russian Federation
2Moscow State Technical University by N.E. Bauman (BMSTU), Faculty of Fundamental Sciences,Department of Applied Mathematics, Russian Federation

###### Abstract

The spread of viral infection occurs mainly as a result of changes in the concentration of virus microparticles in the atmosphere during physical contacts between individuals. The dynamics of changes in the concentration of the pathogenic virus in the individual's body, taking into account accidental physical contacts within the group, is being studied. In the atmosphere of a random cluster of individuals, the concentration of a pathogenic virus changes chaotically. As a result of the diffusion and convective transfer of virus microparticles into the lungs of an individual, the concentration of the virus in the body of the marked individual increases. Depending on the level of concentration of the pathogenic virus that has entered the body, two scenarios of increasing the concentration of the virus are considered. The model assumes that when the virus concentration exceeds the critical value, an explosive increase in the concentration occurs to the maximum value, after which the individual dies. The immune response associated with the generation of antibodies, the concentration of which is proportional to the concentration of the virus, is taken into account. Antibodies increase the critical value of the concentration, exceeding which leads to an exponential increase in the concentration of the virus in the body. If the concentration of the virus in the body is below the critical value, the virus degenerates. The mathematical model consists of a system of stochastic differential equations (SODE) describing the external and internal mechanisms of changes in the concentration of the virus. To simulate the chaotic concentration of the virus in the atmosphere of a cluster of individuals SODE is used that generates a random Gaussian process with an exponentially decaying autocorrelation function. The integral time scale of the autocorrelation function of concentration fluctuations is proportional to the characteristic lifetime of the cluster of individuals. The dynamics of the growth of the concentration of pathogenic virus in the body is based on the model of quadratic growth of concentration and the linear law of destruction of virus microparticles. The maximum value of the virus concentration, the achievement of which leads to the death of an individual, is also taken into account. The equation for the concentration of the virus in the body includes a random source proportional to the difference between the concentration of the virus in the atmosphere in which the individual is located and the concentration of the virus in the body. The system of SODE is studied on the basis of two approaches. The method of direct numerical stimulation (DNS) is based on the numerical solution of a system SODE. The solution methodology of SODE uses modern approaches to solving systems based on modernized Runge-Kutta algorithms. The results of DNS allow us to study in detail the dynamics of changes in the concentration of the virus in the body in various situations. This approach is similar to the Lagrange method in continuum mechanics. In addition, based on the DNS of an ensemble of individuals, the empirical probability density function (PDF) of the distribution of random virus concentration in the body is calculated using methods of mathematical statistics. The analysis of the empirical PDF makes it possible to identify the main trends of the influence of chaotic physical contacts of infected individuals on the dynamics of the spread of the epidemic of viral infection. The second method uses the equation for PDF distribution of the random concentration of the pathogenic virus in the body. This approach is similar to the Euler method in continuum mechanics. Modern methods of applied functional analysis lead to a closed equation for the PDF (the direct Kolmogorov equation) for color noise modeling a random change in the concentration of a pathogenic virus in the atmosphere surrounding the marked individual. To study the closed PDF equation, we use two approaches. First, we have developed a conservative monotone numerical scheme for solution the PDF equation. As a result, we study the dynamics of changes the PDF of the virus concentration in the individual's body. The results of the numerical solution of PDF equation and the empirical PDF obtained by DNS are in satisfactory agreement. Secondly, a system of equations for the first and second moments of fluctuations of the virus concentration in the body is constructed on the basis of a closed PDF equation. The solution of this system of equations for moments gives the dynamics of changes in the averaged parameters of the virus concentration. The solution of this system of equations for moments gives the dynamics of changes in the averaged parameters of the virus concentration. As a result of the study, it is shown that random fluctuations in the concentration of the virus in the atmosphere lead to a qualitatively new behavior of the system, in contrast to the deterministic case. In a random environment, the boundary of the beginning of an explosive increase in the concentration of the virus occurs significantly earlier than follows from the estimates of the deterministic model.

###### Acknowledgements:

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

#### A DFT Study of the Rare Earth-Based Perovskites XAlO3 (X=Gd, Dy or Ho) for photovoltaic applications

Idrissi Samira1

1Mohammed V university of Rabat, Physics, Morocco

###### Abstract

Abstract: In this work, we use the Quantum Espresso code under the pseudo-potentials wave method based on density functional theory (DFT) to investigate the structural, electronic and magnetic properties of the rare earth-based solar perovskites GdAlO3, DyAlO3 and HoAlO3 materials. In fact, the optimized unit cells for such materials have been used to explore the stability of the ferromagnetic behavior of the studied materials. It is found that the cubic perovskite HoAlO3 material is the more stable material. While, the compound DyAlO3 is more stable than GdAlO3 alloy. On the other hand, the band structure and density of states confirm that the GdAlO3 perovskite has a semiconductor nature, while the DyAlO3 and HoAlO3 exhibit a half-metallic character. In addition, the spin-polarized magnetic moments of these compounds reveal that these materials show a ferromagnetic nature. Moreover, the calculated magnetic moments of the cubic GdAlO3, DyAlO3 and HoAlO3 are 7.02 μB, 5.00 μB and 4.00 μB, respectively. Furthermore, the obtained results approve that these compounds could be promising materials for spintronic and optoelectronic devices. Moreover, such materials are promising candidates for photovoltaic applications.

#### Boundary value problems for a higher order Sobolev equation of mixed type

Valery Fedorov1

1North-Eastern Federal University, Scientific Research Institute of Mathematics, Russian Federation

###### Abstract

We study the two boundary value problems for a higher order Sobolev equation of mixed type in a cylindrical domain. Using the regularization method and the Galerkin method, we prove the the regular solvability of the boundary value problem with local boundary conditions. The solvability of the second boundary value problem with an integral boundary condition is reduced to the solvability of the previous problem, but for an integral-differential equation. The regular solvability of this auxiliary problem is proved by the method of consecutive approximations. For both problems, a convergence estimate of the approximate solutions is obtained.

###### Acknowledgements:

This reseach was supported by the Ministry of Science and Higher Education of Russian Federation (project No FSRG - 2020 - 0006).

#### Synthesis of a time-optimal control system for an extremal object

Alexander Pashchenko1

1Institute of Control Sciences of Russian Academy of Sciences, Laboratory of Intelligent control systems and modelling, Russian Federation

###### Abstract

The paper presents the derivation of the synthesis method for the algorithm of the time-optimal controller for a third order dynamic system. A model with an extreme second-order transient response with delay was adopted as an object of research. The constant speed actuator is represented by an integrator. The synthesis is based on using the Pontryagin’s maximum principle and describing the dynamics of a system in the state space using canonical variables. The verification of the correctness of the result obtained by the theorem of Feldbaum A.A. on the number of switchings of the direction of movement of the regulating body during the control interval has been executed. To calculate the canonical state variables, it is proposed to use the position of the regulator, the controlled value and the derivative calculated from its values, measured on real objects.

#### On finite spectrum assignment problem in bilinear control systems with one lumped and distributed delay in state

Vasilii Zaitsev1

1Udmurt State University, Mathematical, Russian Federation

###### Abstract

We consider a bilinear control system defined by a linear time-invariant system of differential equations with the lumped and distributed delay in the state variable. We study a finite spectrum assignment problem by stationary control. One needs to construct constant control vector such that the characteristic quasi-polynomial of the closed-loop system becomes a polynomial with arbitrary preassigned coefficients. We obtain conditions on coefficients of the system under which the criterion was found for solvability of this finite spectrum assignment problem. This criterion is expressed in terms of rank conditions for matrices of the special form. Corollaries on stabilization of a bilinear system with delay are obtained. The results extend the previously obtained results (DOI: 10.20537/vm190102) on spectrum assignment for bilinear systems with only lumped delay

#### Impact of covertly counteracting vehicles on the characteristics of the transport system of a smart city

Nikita Bykov1

1Bauman Moscow State Technical University, Special Machinery, Russian Federation

###### Abstract

The development of smart city transport systems, including self-driving cars, leads to an increase in the threat of interference in vehicle control processes, including with the aim of disrupting the normal functioning of the transport system. In this paper, within the framework of the cellular automata approach, a simulation model of two-lane cyclic movement in a transport system was developed. Model contains two types of agents: conventional vehicles and counteracting vehicles, whose task is to covertly negative influence the traffic flow due to special rules of lane change. It is shown that such counteracting vehicles can affect the system flux mainly in the region of the maximum of the fundamental diagram.

###### Acknowledgements:

The reported study was funded by RFBR, project number 19-29-06090 mk.

#### Geometrical model of diffuse reflection of optical radiation from the surface of biological tissues implemented on the basis of two-dimensional "fractional Brownian motion" process

Artur Smirnov1 , Nikita Kovalenko2 , Oleg Ryabushkin3

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

###### Abstract

The surfaces of biological tissues represent complex spatial structures that are influenced by a variety of vital processes occurring in the body. Recently, it was demonstrated that due to the features of cellular structures, the surface of biological tissues can be described on the basis of the process of fractional Brownian motion (fBm). The fBm parameters (Hurst index H and scale parameter σ) can be considered as the quantitative characteristics of the surface relief. There are several ways to study the surfaces of biological tissues. The conventional methods are optical profilometry (in the visible range of the optical spectrum) and electron microscopy. An alternative method is to measure the intensity of the reflected optical radiation from the surface of biological tissues, which diffuse nature is determined by the relief characteristics. In this work, the mathematical modeling of the reflection of optical radiation from a two-dimensional surface was carried using the Kirchhoff integral: $$E^s = \oint\frac{1}{4\pi}\left[\left(ik + \frac{1}{r}\right)E\cos\alpha-\frac{\partial E}{\partial n} \right] \frac{e^{-ikr}}{r}dF$$ where $E^s$ is the amplitude of electrical component of the diffusely reflected electromagnetic field at a certain point above the surface, $k$ is the wave number, $E$ is the complex amplitude of the field at the surface, $α$ is the angle between the surface normal vector and the radius vector $r ⃗$ from the surface element $dF$ to the point above the surface. As a result of the calculations the intensity distribution of the reflected normally incident Gaussian beam was obtained (the radiation wavelength is 1 μm, the beam waist of 10 μm diameter was located at the distance of 1 mm from the tissue surface). Implementations of the two-dimensional fBm were considered as the surface models. It was shown that the changes of the numerical values of the characteristics of fBm implementations in the vicinity of H = 0.803 and σ = 0.1 (values for the epidermis of the banana fruit) significantly affect the calculated phase reflection functions (angular intensity distribution of reflected radiation). The obtained results reveal that the characteristic parameters of the surface relief can be restored relying on the analysis of diffusely reflected radiation. Simulations of radiation propagation using the Kirchhoff integral together with the representation of the biological tissue surface using the implementation of fBm serve as a tool for such analysis.

#### Numerical simulation of changes in the electrical properties of biological tissues under local heating by laser radiation

Nikita Kovalenko1 , Artur Smirnov2 , Oleg Ryabushkin3

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

#### The R-matrix formalism for two-particle scattering problems

Dragos-Victor Anghel1 , Amanda Teodora Preda2 , George Alexandru Nemnes3

1Research Institute of the University of Bucharest (ICUB), , Romania
2Research Institute of the University of Bucharest (ICUB), , Romania
3Research Institute of the University of Bucharest (ICUB), , Romania

###### Abstract

The R-matrix formalism is extended to include two-particle scattering events. The system is the same as in the case of one-particle R-matrix formalism and consists of a number ($\ge2$) of \textit{leads} connected to a \textit{scattering region}. The particles considered are identical spinless fermions and our approach conserves the anti-symmetry of the wavefunction in the entire system, which opens the possibility to account for asymptotic entangled states. The particles are in an external potential, which is translationally invariant in the leads (up to the interface with the scattering region), and they have also mutual interaction when they are both in the scattering region. Using a proper Ansatz for the two-particle wavefunctions, we obtain a consistent system of equations which yields the coefficients for the two-particle scattering functions expanded in terms of anti-symmetrized products of one-particle scattering functions (when at least one particle is in the leads) or of the two-particle eigenstates of the Hamiltonian (when both particles are in the scattering region).

###### Acknowledgements:

This work was supported by a grant of the Romanian Ministry of Research, Innovation and Digitalization, CNCS - UEFISCDI, project number PN-III-P4-ID-PCE-2020-1142, within PNCDI III

#### Molecular dynamics scheme coupling a physical system and an environment system: mathematical structure and enhanced sampling

Ikuo Fukuda1 , Kei Moritsugu2

1Graduate School of Information Science, University of Hyogo, Japan
2Graduate School of Medical Life Science, Yokohama City University, Japan

###### Abstract

Molecular dynamics (MD) are widely used in chemical, biological, material science to investigate the characteristics of physical system in terms of microscopic descriptions. The equations of motion utilized in MD are described by ordinary differential equation (ODE), typically based on the Newtonian equation and a coupling with external degrees of freedom. The coupling has been utilized to generate the Boltzmann–Gibbs distribution for comparison with the experiment under a constant temperature condition. In our work, we have fully extended this idea for considering an environment system surrounding the original physical system. That is, any environment system described by m-degrees of freedom X can be coupled to the original physical system described by (x, p), and the resulted total system can obey an arbitrary chosen phase-space distribution with the density form of P(x,p;X)f(X). We present a mathematical structure of the developed ODE and discuss the ergodic theoretic description to capture the distribution. The simplest approach is to define X as a heat-bath temperature attached to the original physical system. Some detailed protocol of this scheme and its application to biological systems are presented. An approach for stabilizing the enhanced sampling will also be discussed.

#### Stabilization and synchronization of a new fractional-order 4D chaotic system via feedback controller

Shiva Eshaghi1

1Alzahra University, Tehran, Department of Applied Mathematics, Faculty of Mathematical Sciences, , Iran, Islamic Republic Of

###### Abstract

In this article, we introduce a new fractional-order 4D chaotic system derived from the well-known Lorenz-Haken equations and consider the stability of its equilibria. We investigate chaos control of the fractional-order system by means of Lyapunov stability and feedback control technique. We then design control laws to synchronize two identical chaotic fractional-order systems. Further, we reveal complex behaviors of the system numerically.

#### Numerical solution of generalized fractional Volterra integro-differential equations via approximation the Bromwich integral

Shiva Eshaghi1

1Alzahra University, Tehran, Department of Applied Mathematics, Faculty of Mathematical Sciences, , Iran, Islamic Republic Of

###### Abstract

In this paper, we consider the generalized fractional Volterra integro-differential equations with the regularized Prabhakar derivative and represent the solution of this type of equations in the form of Bromwich integral in the complex plane. Then we select the hyperbolic contour as an optimal contour to approximate the Bromwich integral. Further, an example to show absolute errors for various parameters by using our numerical scheme on hyperbolic contour is given.

#### Mathematical modelling of fluid flow through porous media with heterogeneity of permeability

1Samara State Technical University, Oil and Gas Fields Development, Russian Federation

###### Abstract

In this paper the mathematical model of coupled problem for fluid flow in the reservoir with hydraulically fractured well will be discussed. The new boundary condition is taken in to account for modelling of different cases of fractured wells location and for the prediction of water tracer lines. The analytical solution for flow potential will help petroleum engineers to predict well productivity and evaluate the most effective well pattern for waterflooding production system with massive hydraulic fracturing.

###### Acknowledgements:

This work is performed on the grant of the Russian Science Foundation (Project № 15-17-00019). The authors express too their gratitude to Andrey Kasatkin for performing calculations in his software package (The certificate on the state registration of the computer program №2015610136).

#### A NOVEL MULTI-SCALE MODEL FOR SOLID-GAS REACTIONS USING BIVARIATE POPULATION BALANCE EQUATIONS: APPLICATION TO THE COAL CHAR GASIFICATION

Farid Chejne1 , Juan Maya2

1Universidad Nacional de Colombia, Escuela de Procesos y Energía, Colombia
2Universidad Nacional de Colombia, Escuela de Procesos y Energía, Colombia

###### Abstract

In this paper, it is developed a novel mathematical model for solid-gas reactions that simultaneously takes into account the variation of both the internal energy distribution of particles and the particle size. This was achieved by using bivariate population balance equations considering the mean particle temperature and the particle radius as internal coordinates. The model considers the mass and energy transfer phenomena on three spatial scales: pore, intraparticle, and interparticle. Additionally, it takes into account the non-uniformity of the particle microstructure, and the phenomenon of percolative fragmentation. Thus, it can be said that this is the most detailed model for solid-gas reactions developed to date. Finally, the simulations were successfully validated with experimental data on the coal char gasification with CO2 in a fixed bed reactor, and it was found that not taking into account the distribution of mean particle temperature leads to significant errors in the calculation of the energy balance within the reactor.

###### Acknowledgements:

The authors wish to thank the project "Strategy of transformation of the Colombian energy sector in the horizon 2030" funded by the call 788 of Minciencias Scientific Ecosystem, Contract number FP44842-210-2018.

#### Implementing the basic CT backprojecting algorithm in android mobile application

Arman Kussainov1

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

###### Abstract

We have implemented the basic steps for the FDK backprojecting algorithm including the data storage and retrieval, OpenCV libraries import and implementing the application of FFT, frequency space image filtering, image brightness, contrast and quality manipulation. Calculation intensive part of the application was moved to the asynchronous task hosted by a fragment which allows the task to survive the configuration changes and to run in background. The minimalistic interface with the access to all backprojecting parameters was implemented as well. The result of backprojection is saved as an image in phone’s Download folder.

#### Derivation of the Symmetric Stress-Energy-Momentum Tensor in Exterior Algebra

Ivano Colombaro1 , Josep Font-Segura2 , Alfonso Martinez3

1Universitat Pompeu Fabra, Department of information and communications technology, Spain
2Universitat Pompeu Fabra, Department of information and communications technology, Spain
3Universitat Pompeu Fabra, Department of information and communications technology, Spain

###### Abstract


#### CNF-SAT Modeling for banyan-type networks and its application for assessing the rearrangeability

Satoru Ohta1

1Toyama Prefectural University, Department of Information Systems Engineering, Faculty of Engineering, Japan

###### Abstract

A banyan-type network is a switching network. It is constructed by placing unit switches with two inputs and two outputs in $s$ ($s > 1$) stages. In each stage, $2^{n − 1}$ ($n > 1$) unit switches are aligned. This configuration provides a switch with $2^n$ inputs and $2^n$ outputs. These inputs and outputs are indexed $0, 1, \ldots, 2^n – 1$. Then, the indices of outputs requested to connect inputs $0, 1, \ldots, 2^n – 1$ is represented as a permutation of $0, 1, \ldots, 2^n – 1$. The route from input to destination output must be determined appropriately for a given permutation by setting the connection states of unit switches. When $s = n$, routing is simple because there is only one path between an input and output. However, when $s = n$, the network causes blocking. Thus, the network can establish connections only for a limited number of permutations. The past study suggests that the network becomes rearaangeablly nonblocking (or rearrangeable, in short) when $s \ge 2n – 1$. In other words, the network can establish connections for any given permutations if a sufficiently large number of stages are provided. Unfortunately, the routing algorithm is unclear for such a network except for a few cases. Moreover, although a considerable number of theoretical analyses have been done, the rearrangeability of the banyan-type network with $2n – 1$ or more stages is not entirely proved. As a tool to tackle these problems, this study presents a CNF-SAT modeling scheme for banyan-type networks. In this scheme, the routing for a given permutation is formulated to a SAT (satisfiability) problem represented in CNF (conjunctive normal form). Whether the problem is satisfiable or unsatisfiable is determined by feeding it to a SAT solver. The network is not rearrangeable if the problem is unsatisfiable for a specific permutation. By contrast, if the problem is satisfiable for any permutations, the network is rearrangeable. Moreover, if the problem is satisfiable, routing is also determined using variable values that satisfy the propositional logic. This study applies the CNF-SAT modeling scheme to several configurations of $2n – 1$ stage banyan-type networks and randomly generated permutations. The networks are built based on the link configurations found in banyan and baseline networks. Consequently, some of examined $2n – 1$ stage networks are not rearrangeable. Furthermore, a common characteristic is found in the link configurations for the networks that are (almost certainly) rearrangeable. The discovery of this characteristic will be helpful to conduct future theoretical studies on the connection capability of banyan-type networks.

###### Acknowledgements:

This work was supported by JSPS KAKENHI Grant Number JP19K11928. The author would like to thank Enago (www.enago.jp) for the English language review.

#### Quantum computational methods to investigate the electrochemical stability of ionic liquids for lithium-ion cells.

Annalisa Paolone1 , Sergio Brutti2

1Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, Italy
2Sapienza University of Rome, Department of Chemistry, Italy

###### Abstract

A Paolone 1 and S Brutti 1,2,3 1 Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, Piazzale A. Moro 5, I-00185 Roma, Italy 2 Sapienza Università di Roma, Dipartimento di Chimica, Piazzale A. Moro 5, I-00185 Roma, Italy 3 GISEL - Centro di Riferimento Nazionale per i Sistemi di Accumulo Elettrochimico di Energia, INSTM, via G. Giusti 9, I-50121 Firenze, Italy The electrochemical stability windows of selected ionic liquids have been calculated by comparing different computational approaches, previously proposed in the literature. The computational results have been discussed in close comparison with the available experimental data. The molecular systems under study are based on di-alkyl imidazolium and tetra-alkyl ammonium cations coupled with two different imide anions (namely, bis-fluorosulfonyl imide and bis-trifluoromethyl sulfonyl imide). Thermodynamic oxidation and reduction potentials have been estimated either on single ions or on the ionic couples, through vertical or adiabatic electron exchange transitions. Furthermore, the effect of implicit solvent has been considered. We previously provided evidence that despite the crude approximation, the electrochemical stability windows of ionic liquids are well predicted by the MP2 theory considering a vertical transition in vacuum without including either vibrations or solvation [1]. In the present study we investigated whether DFT calculations could be used instead of the more computationally expensive MP2 model. Calculations of the electrochemical stability of the previously investigated anions were performed by various DFT functional and compared to both the MP2 results and the experimental values [2] obtained for the corresponding ionic liquids. Various DFT functional were exploited with various levels of complexity, ranging from those based on the simples Generalized Gradient Approximation (GGA) to those relying on the Range Separated Hydrid meta-Generalized Gradient Approximation (RSH-mGGA). Indications about the best performing functionals are given. References [1] Paolone, A.; Brutti, S.Comparison of the Performances of Different Computational Methods to Calculate the Electrochemical Stability of Selected Ionic Liquids. Materials 2021, 14, 3221. [2] Brutti, S.; Simonetti, E.; de Francesco, M.; Sarra, A.; Paolone, A.; Palumbo, O.; Fantini, S.; Lin, R.; Falgayrat, A.; Choi, H.; et al. Ionic Liquid Electrolytes for High-Voltage, Lithium-Ion Batteries. J. Power Sources 2020, 479, 228791.

###### Acknowledgements:

Acknowledgements The authors would like to acknowledge the financial support from the European Union Horizon 2020 research and innovation programme within the Si-DRIVE project, grant agreement No 814464.

#### Bright Bound Soliton Molecules in Spin-1 Bose-Einstein Condensates with Non-autonomous Nonlinearities

Karuppaiya Sakkaravarthi1 , R Babu Mareeswaran2 , T Kanna3

1Asia Pacific Center for Theoretical Physics (APCTP), Physics, Korea, Republic of
2PSG College of Arts and Science, PG & Research Department of Physics, India
3Bishop Heber College (Autonomous), PG & Research Department of Physics, India

###### Abstract

This work deals with matter-wave bright soliton molecules in spin-1 Bose-Einstein condensates governed by three-coupled Gross-Pitaevskii equations with non-autonomous nonlinearities that can be tuned by Feshbach resonance management. Particularly, it portrays the possible generating mechanism of bright bound soliton molecules with the help of an exact analytic solution under a controlled velocity environment. Results show that these bound molecules experience the effects of time-varying nonlinearities and modulate themselves during propagation by keeping their stable properties. Significantly, the chosen periodic and kink-like nonlinearities expose the snaking and single-step compressed-amplification of multi-structured bound soliton profiles along with appreciable changes in their amplitude, velocity, and width. The presented results will be substantial addition towards a complete understanding beyond the known interaction dynamics of matter-wave bright solitons in spinor condensates.

###### Acknowledgements:

KS was supported by Asia-Pacific Center for Theoretical Physics (APCTP) as a Postdoctoral Researcher through Young Scientist Training (YST) program.

#### On Symmetric Solutions to Linear Matrix Time-Varying Differential Equations

Dmitry Fetisov1

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

###### Abstract

In this paper, we deal with a problem of the solutions symmetry for linear matrix time-varying differential equations. Throughout the paper, we assume that the coefficients in the equation are of finite order of smoothness. To verify whether a solution of the initial value problem is symmetric on a given interval, we propose to construct a special matrix sequence. Using the sequence, we prove a sufficient condition for the solution symmetry on a given interval. Under the above condition, we establish a formula for a symmetric solution to a linear matrix time-varying differential equation.

###### Acknowledgements:

This work was supported by the Russian Foundation for Basic Research (projects 20-07-00279 and 19-07-00817).

#### Model of collisions between magnetic nanoparticles and the arterial wall

Daniela Garzón Suárez 1 , Luz H Camargo2 , Diego Rodríguez Patarroyo3

1Universidad Distrital Francisco José de Caldas, Faculty of Engineering, Colombia
3Universidad Distrital Francisco José de Caldas, Faculty of Engineering, Colombia

###### Abstract

At present, there are different treatments against cancer, however, some of them, such as chemotherapy, are very invasive for the human body, since they affect healthy tissues. Magnetic targeting of drugs by means of magnetic nanoparticles is one of the alternative techniques that have emerged in the last decade, it is based on the targeting of drug delivery to the tumor without affecting healthy tissues, via of injected nanoparticles with diamagnetic properties directly into the bloodstream, driven by external magnetic fields produced by permanent magnets. This technique in literature is often come upon as MTD for its acronym in English. In this work, a numerical the model was developed in order to quantify the loss of nanoparticles in the process of interaction with the walls of the bloodstream. For this model, the Monte Carlo Kinetic the technique was used, quantifying the probability of adsorption and absorption taking into account the following parameters: diameter of the nanoparticle (200 nm), the density of the nanoparticle (6450 kg m-3), the diameter of the cell endothelial (0.1 μm - 1 μm), transcellular pores of the fenestrated endothelium (70 nm) and modulus of elasticity of the endothelium (4.1 ± 1.7 kPa).

#### Thermodynamic analysis of oligomeric blends applying Kirkwood-Buff theory of solutions

Fotis Venetsanos1 , Stefanos Anogiannakis2 , Doros Theodorou3

1National Technical University of Athens, Chemical Engineering, Greece
2National Technical University of Athens, Chemical Engineering, Greece
3National Technical University of Athens, Chemical Engineering, Greece

###### Abstract

The accurate prediction of the thermodynamic properties of oligomeric blends and, in general, binary liquid mixtures from atomistic simulations is a challenging task. In this work we develop a methodology for the full thermodynamic analysis of oligomeric blends and the extraction of the Flory-Huggins interaction parameter from the Gibbs energy of mixing, combining Flory-Huggins thermodynamics with Kirkwood-Buff theory of solutions. We perform a series of Molecular Dynamics (MD) simulations of 2-methylpentane/n-heptane mixtures, at various mole fractions. Firstly we validate the forcefield we apply in our MD simulations, comparing the density and excess volume we obtain against the corresponding experimental estimates found in the literature. Then we calculate the Kirkwood-Buff integrals in the isothermal-isobaric (NpT) ensemble, applying the particle fluctuations method, and we extract the component activity coefficients, the excess Gibbs energy, the excess enthalpy, and the excess entropy of mixing as functions of the mole fraction. Finally we calculate the Flory-Huggins interaction parameter χ by interpreting the Gibbs energy of mixing in the framework of Flory-Huggins theory, and explore its dependence on composition. All results are compared against experimental measurements in order to evaluate our methodology. Agreement is found to be very good.

###### Acknowledgements:

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

#### Determination of ship roll damping coefficients by a differential evolution algorithm

1University of Strathclyde, Naval Architecture and Ocean Engineering, United Kingdom
2Nasdis pds d.o.o., , Slovenia

###### Abstract

The execution of the so-called extinction tests represents the classical experimental method used to estimate the damping of an oscillatory system. For the specific case of ship roll motion, the roll decay tests are carried out at model-scale in a hydrodynamic basin. During these tests, the vessel is posed in an imbalance condition by an external moment and, after the release, the motion decays to the equilibrium condition. When the damping is far below the critical one, the transient decay is oscillatory. Here a new methodology is presented to determine the damping coefficients by fitting the roll decay curves directly, using a least-square fitting through a differential evolution algorithm of global optimisation. The results obtained with this methodology are compared with the predictions from standard methods. This kind of approach seems to be very promising when the motion model of the system under investigation is established with any level of non-linearities included. The usage of the fitting procedure both on the numerical solution and the approximate analytic solution of the differential equation of motion demonstrates the flexibility of the method. As a benchmark example, two experimentally measured roll extinction curves have been considered and suitably fitted. The newly predicted results, compared with the ones obtained from standard roll decay analysis, show that the algorithm is capable to perform a good regression on the measured data.

#### Molecular Dynamics Simulations of PE Bilayers in the Melt State

Nikolaos Romanos1

1NTUA, Chemical Engineering, Greece

###### Abstract

Molecular Dynamics Simulations of PE Bilayers in the Melt State Nikolaos Romanos, Grigorios Megariotis,* and Doros N. Theodorou School of Chemical Engineering, National Technical University of Athens (NTUA), 9 Heroon Polytechniou Street, Zografou Campus, Athens GR-15780, Greece Abstract By combining two different films of polyethylene (PE) melts we study the structural and dynamical properties of these subsystems via molecular dynamics (MD) simulations. Each film is comprised of chains with different molar mass, yet the same chemical constitution. Having already studied the same properties at temperatures between the glass transition temperature and melting point, we extend this work to the fully molten state. Materials made from polyolefins of the same chemical constitution but different molar mass are important in packaging applications that combine good properties with sustainable recycling after their disposal. Initially, two independent PE thin films are constructed using an “amorphous builder” which constructs the chains bead by bead (united atom). The TraPPE united atom force field is used at a temperature of 450 K. The system made by joining the two films is called a slab; it is replicated in all three directions using periodic boundary conditions. The slab is first energy minimized and then subjected to NPT molecular dynamics simulation at 450 K and 1 bar for 2 μs. We study structural and dynamical properties of the films such as the self-diffusion coefficient of the chain centers of mass, and mass density profiles. ____________ *To whom any correspondence should be addressed: gregm@mail.ntua.gr

#### Generation of new symmetries from an explicit symmetry breaking

Nikolaos Dimakis1

1Sichuan University, College of Physics, China

###### Abstract

We study how the explicit symmetry breaking, through a continuous parameter in the Lagrangian, can actually lead to the creation of different types of symmetries. As examples we consider the motion of a relativistic particle in a curved background, where a non-zero mass breaks the symmetry of the conformal algebra of the metric and, the motion in a Bogoslovsky-Finsler spacetime, where a Lorentz violation takes place. In the first case, new non-local conserved charges emerge in the place of those which were previously generated by the proper conformal Killing vectors, while in the second, rational in the momenta integrals of motion appear to substitute the linear expressions corresponding to those boosts which fail to be symmetries.

#### A numerical analysis to improve efficiency of a short-dwell blade coaters with the help of wall heating

Bapuji Sahoo1 , Bikash Mahato2 , T. V. S. Sekhar3

1IIT Bhubaneswar, School of Basic Sciences ( Mathematics ), India
2Indian Institute of Technology Bhubaneswar, School of basic Sciences (Mathematics), India
3IIT Bhubaneswar, School of Basic Sciences ( Mathematics ), India

###### Abstract

Blade coaters are most commonly used for coating of paper and paperboard with higher efficiency. Short-dwell blade coaters are the specifically designed blade coater used for high-speed and uniform coating. However, the trend to increase machine speed and reduction in coat weight has increased the difficulty of attaining uniform coat weight profiles on the blades. The efficiency of short-dwell blades coaters depends on many factors such as the properties of the coating material, design of the coating reservoir, the types of flow behaviour taking place inside the reservoir, etc. In this work, we have proposed an optimal design of the reservoir to improve the efficiency of short-dwell coaters. The reservoir has been modelled as flow inside a two-dimensional rectangular cavity. The efficiency of the coaters has been further improved by incorporating the buoyancy effect into the flow by maintaining walls of the cavity at different temperatures. Incompressible Navier-Stokes equations in primitive variable formulation have been solved to obtain the flow fields inside the cavity. Spatial derivatives present in the momentum, continuity and energy equations are evaluated using a fourth-order accurate compact scheme whereas the temporal derivatives are calculated using the fourth-order Runge-Kutta method. The actual rate of convergence of the numerical scheme has been discussed in details. In addition, the accuracy and stability of the used numerical method are also analysed in the spectral plane with the help of amplification factor and group velocity contour plot. The obtained numerical solutions have been validated with the existing literature. The flow parameters have been optimized considering rectangular cavities of different aspect ratios and for various thermal conditions.

###### Acknowledgements:

Prof. T. V. S. Sekhar would like to express thanks to SERB Government of India for supporting a part of this research work through project Grant vide File No. CRG/2019/000458/MS dated 18.01.2020.

#### OPTIMAL EMISSION CONTROL AND IDENTIFICATION OF AN UNKNOWN POLLUTION SOURCE

David Parra-Guevara1 , Yuri Skiba2

1National Autonomous University of Mexico, Center for Atmospheric Sciences, Mexico
2Universidad Nacional Autónoma de México (UNAM), Centro de Ciencias de la Atmósfera (Centre for Atmospheric Sciences), Mexico

###### Abstract

The advection-diffusion-reaction equation is used for describing the dispersion of a quasi-passive contaminant from industrial point sources in a limited area. The conditions established on the open boundary ensure that the problem is correct in the sense of Hadamard, that is, its solution exists, is unique, and is stable to initial perturbations. The Lagrange identity is used to construct the adjoint operator and formulate an adjoint problem. Equivalent direct and adjoint estimates are derived to assess the concentration of the pollutant at monitoring sites of the area. Formulas obtained on the basis of adjoint estimates are useful in analyzing the sensitivity of the model to both variations in the intensity of pollution sources and variations in the initial distribution of the pollutant concentration in the area. New optimal emission control strategies based on using the adjoint estimates are developed in order to prevent violations of existing sanitary standards by timely reduction of emission rates of operating sources. Optimal control here lies in minimizing these reductions. In addition, this control is primarily aimed at reducing the intensity of emissions from sources that most pollute the monitoring site. Also, new methods are proposed for identifying the main parameters of an unknown point source that arose as a result of a dangerous incident (accident, explosion, etc.). These methods allow determining the location and intensity of a constant or non-stationary point source, as well as the moment of emission of a pollutant in the case of an instantaneous point source. This helps to quickly assess the scale of the incident and its consequences. Numerical results show the effectiveness of the methods.

###### Acknowledgements:

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

#### Gravity assists gravitational scattering and the perturbation rings in the Solar system

Alexey Grushevskii1

1Keldysh Institute of Applied Mathematics of RAS, Space Flight Mechanics, Russian Federation

###### Abstract

One of the types of gravitational scattering in the Solar system within the framework of the model of the restricted three-body problem (R3BP) is gravity assist maneuvers of the "particles of insignificant mass" [1] (spacecraft, asteroids, comets, etc.) . For their description, a physical analogy with the beam scattering of charged α particles in a Coulomb field is useful. However, unlike the scattering of charged particles, there are external restrictions for the possibility of gravity assists executing related from the restricted size of planet's sphere of influence. At the same time, internal restrictions for the gravity assists performance estimated by the effective radii of planets are known from the literature on R3BP [2] (gravitational capture by the planet, falling into it). They depend from the particle asymptotic velocity relative the planet. For obvious reasons, their influence cuts off the possibility of effective gravity assists performance [3]. In this work the generalized estimates of the sizes of the near-planetary regions ("perturbation rings"), falling into which is a necessary condition for the implementation of gravity assists, are presented. The detailed analysis shows that Neptune and Saturn have the characteristic "perturbation rings" of the largest sizes in the Solar system, and Jupiter occupies only the fourth place in the list. References [1] Szebehely V 1967 Theory of Orbits. The Restricted Problem of Three Bodies. Academic Press, New York [2] Labunsky A et al 1998 Multiple Gravity Assist Interplanetary Trajectories Earth Space Institute Book Series (London: G&B) [3] Golubev Yu, Grushevskii A et al Solar System Research, 2020, 54, pp 318–328

#### Accelerating the charge inversion algorithm with hierarchical matrices for gas insulated systems

Francesco Lucchini1 , Nicolò Marconato2

1Università degli Studi di Padova - Centro Ricerche Fusione, Consorzio RFX, Italy
2University of Padova, Department of Industrial Engineering, Italy

###### Abstract

Surface charges accumulating on dielectrics during long-time operation of Gas Insulated High Voltage Direct Current (HVDC-GIS) equipments may affect the stable operation and could possibly trigger surface flashovers. In industrial applications, to quantify and identify the location of the surface charge accumulation from experimental measurements, the surface potential distribution is evaluated using, e.g., electrostatic probes, then the charge density is determined by solving an electrostatic problem based on an inversion procedure known as Charge Inversion Algorithm. The major practical limitation of such procedure is the inversion and the storage of the fully dense matrix arising from the representation via Integral Equations of the electrostatic phenomenon, resulting in O(N^3) computational complexity and O(N^2) memory requirement. In this paper it is shown how hierarchical matrices can be efficiently used to accelerate the charge inversion algorithm and, more importantly, reduce the overall memory requirement.

#### A comparison between current-based integral equations approaches for eddy current problems

Francesco Lucchini1 , Nicolò Marconato2

1Università degli Studi di Padova - Centro Ricerche Fusione, Consorzio RFX, Italy
2University of Padova, Department of Industrial Engineering, Italy

###### Abstract

In this paper, a comparison between two current-based Integral Equations approaches for eddy current problems is presented. In particular, the very well-known and widely adopted loop-current formulation (or electric vector potential formulation) is compared to the less common $\mathbf{J}$-$\varphi$ formulation. Pros and cons of the two formulations with respect to the problem size are discussed, as well as the adoption of low-rank approximation techniques. Although rarely considered in the literature, it is shown that the $\mathbf{J}$-$\varphi$ formulation may offer some useful advantages when large problems are considered. Indeed, for large-scale problems, while the computational efforts required by the two formulations are comparable, the $\mathbf{J}$-$\varphi$ formulation does not require any particular attention when non-simply connected domains are considered.

#### Rutherford's extended formula for the gravitational scattering and the synthesis of gravity assists chains in the Solar system

Alexey Grushevskii1

1Keldysh Institute of Applied Mathematics of RAS, Space Flight Mechanics, Russian Federation

###### Abstract

Rutherford's formula for the scattering of charged α particles in the Coulomb field can be easily generalized to the case of gravitational scattering. The extended Rutherford formula for the gravitational scattering is presented. One of the types of the gravitational scattering in the Solar system is the gravity assist maneuvers. In this paper, an effective gravitational scattering cross-section is introduced by analogy for them and the generalized Rutherford formula for gravitational scattering is presented out when performing gravity assists. Modern methods of the ballistic design of the interplanetary space flights using gravity assist maneuvers around planets [1-3] are associated with the need to calculate a lot of trajectories (i.e. of the phase beams). For their effective use it is necessary to study the structure of non-linear flyby gravitational scattering using the Rutherford’ formula and to construct the corresponding effective modelling using according regularized phase beams. It is shown that with using of such approach, it is possible to significantly increase the efficiency of the recurrent procedure for the gravity assists chains searching for ballistic scenarios of the modern interplanetary flights

#### Identifying steady-states in a biophysical model of cell swelling

Vincent Ouellet1 , Julia Price2 , Nicolas Doyon3 , Antoine Godin4 , Pierre Marquet5

1Université Laval, Département de psychiatrie et de neurosciences, Canada
2Université Laval, Département de mathématiques et de statistique, Canada
3Université Laval, Département de mathématiques et de statistique, Canada
4Université Laval, Département de psychiatrie et de neurosciences, Canada
5Université Laval, Département de psychiatrie et de neurosciences, Canada

###### Abstract

Biophysical models based on systems of ordinary are often used to describe the electrical activity and/or ionic homeostasis of cells such as neurons and astrocytes. Current mathematical models often overlook transmembrane water fluxes which nevertheless play important roles in regulating cell volume and osmolarity. We here analyze a mathematical model based on biophysical principles to describe the ionic and volume responses of neurons. Our model consists of 4 ODEs and an algebraic equation and is given by the different ionic fluxes J : \begin{align*} \frac{\mathrm{d}n_{Na}}{\mathrm{d}t} &=-\left(J_{Na,p} + 3 J_{pump} + J_{NKCC1}+J_{KCC2}\right),\\ \frac{\mathrm{d}n_{K}}{\mathrm{d}t} &=-\left(J_{K,p} -2 J_{pump} + J_{NKCC1}+J_{KCC2}\right),\\ \frac{\mathrm{d}n_{Cl}}{\mathrm{d}t} &=-\left(J_{Cl,p} + 2 J_{NKCC1}+J_{KCC2}\right),\\ \frac{\mathrm{d}w}{\mathrm{d}t} &= \Pi \left(\mbox{Osm}_i - \mbox{Osm}_o\right),\\ 0&=\left[Na\right]_i + \left[K\right]_i -\left[Cl\right]_i - \left[An\right]_i, \end{align*} We rigorously determine the fixed points of the system and identify conditions under which the cell has only one steady-state. Further, when inserting voltage-gated channels in our models, we establish conditions for the existence of multiple equilibria. It is often assumed that initial conditions correspond to the steady-state of the system but how to find this steady-state is rarely addressed in the literature, we here propose a solution to this problem.

###### Acknowledgements:

Authors would like to acknowledge the financial support of the Canada Excellence Research Chair in Neurophotonics (Pierre Marquet). Antoine G. Godin is a Scholar of the Fonds de recherche du Québec – Santé and was supported by a Sentinel North Partnership Research Chair and grant #06507 from the Natural Sciences and Engineering Research Council of Canada.

#### Thermodynamic Analysis of the Relaxation Model for Non-Equilibrium Phase Behavior of Hydrocarbon Mixtures

Ilya Indrupskiy1

1Oil and Gas Research Institute of Russian Academy of Sciences, S.N. Zakirov Lab of Gas, Oil, and Condensate Recovery, Russian Federation

###### Abstract

Mathematical models of phase behavior are widely used to describe multiphase oil and gas-condensate systems during hydrocarbon recovery from natural petroleum reservoirs. Previously a non-equilibrium phase behavior model was proposed as an extension over generally adopted equilibrium models. It is based on relaxation of component chemical potentials difference between phases and provides accurate calculations in some typical situations when non-instantaneous changing of phase fractions and compositions in response to variations of pressure or total composition is to be considered. In this paper we present a thermodynamic analysis of the relaxation model. General equations of non-equilibrium thermodynamics for multiphase flows in porous media are considered, and reduced entropy balance equation for the relaxation process is obtained. Isotropic relaxation process is simulated for a real multicomponent hydrocarbon system with different values of characteristic relaxation time using the non-equilibrium model implemented in the PVT Designer module of the RFD tNavigator simulation software. The results are processed with a special algorithm implemented in Matlab to calculate graphs of the total entropy time derivative and its constituents in the entropy balance equation. It is shown that the constituents have different signs, and the greatest influence on the entropy is associated with the interphase flow of the major component of the mixture and the change of the total system volume in the isotropic process. The characteristic relaxation time affects the rate at which the entropy is approaching its maximum value.

###### Acknowledgements:

This study is a contribution to the research program under the State Research Contract of OGRI RAS (topic AAAA-A19-119022090096-5). The authors acknowledge the possibility to use the RFD tNavigator software under the academic license.

#### Adjoint Numerical Method for a Multiphysical Inverse Problem of Two-Phase Well Testing in Petroleum Reservoirs

Ilya Indrupskiy1

1Oil and Gas Research Institute of Russian Academy of Sciences, S.N. Zakirov Lab of Gas, Oil, and Condensate Recovery, Russian Federation

###### Acknowledgements:

The study is a contribution to the research program under the State Research Contract of OGRI RAS (topic AAAA-A19-119022090096-5)

#### One-dimensional thermal equation modeled on a two-dimensional heat exchanger with variable solid-fluid interface

Hideshi ISHIDA1 , Koichi HIGUCHI2 , Taiki HIRAHATA3

1Setsunan University, Department of Mechanical Engineering, Japan
2Setsunan University, Department of Mechanical Engineering, Japan
3Setsunan University, Department of Mechanical Engineering, Japan

###### Abstract

The solid-to-liquid heat transfer around heat exchangers has been intensively investigated. Such a coupled analysis involves different time-spatial scale of heat transfer for each phase, needing time-consuming computations. In particular, it is noticeable when the heat exchanger has complicated shape. In this study, we are to present that a one-dimensional equation for vertically averaged temperature, modeled on a vertically thin, two-dimensional heat exchanger with variable top solid-fluid interface, recovers the two-dimensional thermal information, i.e. steady temperature and flux distribution on the top and temperature-fixed bottom faces. The relative error of these quantities is less than 5% with the product of the representative height of the exchanger and the maximum gradient of the height kept below 0.5, while the computational time is reduced to 0.1~5%, when compared with direct two-dimensional computations, depending on the shape of the top face. The model equation, derived by the vertical averaging of the two-dimensional thermal conduction equation, is closed by an approximation that the heat exchanger is sufficiently thin in the sense that the second derivative of temperature with respect to the horizontal coordinate depends only on the coordinate. In this model equation, the fluid equation, i.e. the Navier-Stokes equation, above the exchanger is decoupled by a conventional equation for non-dimensional heat fluxes on the top surface, a Robin boundary condition. In principle, however, the coupling of the model with the fluid equation is possible through the temperature and heat flux on the top interface, recovered by the model equation. The type of mathematical modeling can be applicable to a wide variety of bodies with extremely small dimensions in some (coordinate-transformed) directions.

###### Acknowledgements:

This work is supported by JSPS KAKENHI Grant Number JP20K04317.

#### Frequency analysis in an infinite beams array

Hugo Aya Baquero1

###### Abstract

This model consists of a periodic fluid structure formed by solid beams equidistant from each other submerged in a fluid. The beams are clamped at both ends. The distance between the beams, the mechanical properties of the solid and the fluid; and the geometric parameters of the beams determine a relationship between the frequencies of the mechanical waves that can propagate through the structure and the wave vector. Analysis within the first Brillouin zone with the Bloch periodicity condition gives rise to frequency bands in which there is propagation of mechanical waves and bands in which no waves are propagated. Several propagation bands and some forbidden regions were found in the examined frequency ranges for various geometric configurations.

###### Acknowledgements:

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

#### The Effect of Problem Situation Teaching on Students’ Mathematical Problem Solving under the Key Competency Reform in High School

ZHIPENG REN1

1THE UNIVERSITY OF HONG KONG, Faculty of Education, Hong Kong

###### Abstract

Students’ problem-solving ability has gained much attention in mainland China under the ongoing key competency reform in high school. Students in high school should apply their learning outcomes to solve various problems in their daily life. This study aims to examine the mechanism of problem situation teaching influencing students’ problem-solving activities. A combination of quantitative and qualitative research methods have been applied in this study: experiment method, case analysis, quantitative method, and interview method. This study draws the conclusion that problem situation learning experience can help students solve related applied questions, and the score of the problem-solving test is significantly improved; the mechanism of problem situation teaching influencing students’ problem-solving activities is found as 3 aspects. This study expects that teachers can improve their teaching activities under the reform of key competency by undertaking some strategies.

#### Semi-Analytical Method for Accurate Calculation of Well Injectivity During Hot Water Injection for Heavy Oil Recovery

Ilya Indrupskiy1

1Oil and Gas Research Institute of Russian Academy of Sciences, S.N. Zakirov Lab of Gas, Oil, and Condensate Recovery, Russian Federation

###### Abstract

Representation of wells in numerical simulation of petroleum reservoirs is a challenging task due to large difference in typical scales of grid blocks (tens to hundreds meters) and wells (~0.1 m), with high pressure and saturation gradients around wells. Although a variety of grid refinement techniques can be used for local simulations, they have limited application in field-scale problems due to huge model dimensions. Thus, auxiliary quasi-stationary local solutions (so-called inflow performance relations) are used to relate well flow rate with well and grid block pressures. These auxiliary solutions are strictly derived for linear cases and generalized to non-linear problems by using grid-block averaged values of fluid and reservoir properties. In the case of hot water injection for heavy oil recovery, this results in significant errors in well injectivity calculations due to large temperature and saturation gradients dynamically influencing viscosity and relative permeability distributions around the well. In this paper we propose a method which combines a semi-analytical solution of the hyperbolic Entov-Zazovsky problem for non-isothermal oil displacement with integration for pressure distribution taking into account nonlinear dependencies of fluid viscosities and relative permeabilities on temperature and saturations. Both constant injection rate and constant well pressure cases are considered. Example calculations demonstrate that the method helps to avoid underestimation of well injectivity in non-isothermal problems caused by grid-block averaging of fluid and reservoir properties in conventional inflow performance relations.

###### Acknowledgements:

The study is a contribution to the research program under the State Research Contract of OGRI RAS (topic AAAA-A19-119022090096-5)

#### Application of the form invariance transformations of the scalar cosmological model in inflation theory

Olga Razina1 , Pyotr Tsyba2 , Nurgul Suikimbayeva3

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

###### Abstract

In this work, it is shown that the equations of motion of the scalar field for spatially flat, homogeneous, and isotropic space-time Friedmann-Robertson-Walker have a form-invariance symmetry is arising from the form-invariance transformation. Form-invariance transformation is defined by linear function $\bar{\rho}=n^2\rho$. It is shown the method of getting potential and the scalar field for the power law scale factor. The initial model is always stable at $\alpha>1$, but the stability of the transformation model depends on index $n$. Slow roll parameters and spectral induces is obtained and at large $\alpha$ they agree with Planck observation data.

###### Acknowledgements:

This study was funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan AP08955524.

#### Parameter estimation for a simplified model of an electrolytic capacitor in transient regimes

Corneliu Barbulescu1 , Toma-Leonida Dragomir2

1Universitatea Politehnica Timisoara, Facultatea de Automatica si Calculatoare, Romania
2Universitatea Politehnica Timisoara, Facultatea de Automatica si Calculatoare, Romania

###### Abstract

Real capacitors' behavior in electric circuits deviates from the ideal one, modeled by a single capacity. In order to find better compromises between precision and simplicity, different models are used starting with the C-R series circuit and continuing with some other C-R-L models (capacitances connected with resistances and/or inductances in series and/or parallel circuits). In these models, C, R, L are called equivalent parameters and take constant values. According to this point of view, the capacitors are modeled as lumped parameter subsystems even it is well known that the real capacitors are essentially distributed parameter systems. Moreover, as highlighted in this paper, the capacitors are also time-variant subsystems. In the literature, this issue is not explicitly discussed although the frequency characteristics of ESR (Equivalent Series Resistance) and equivalent capacitance of capacitors, available in datasheets, suggest the time-varying behavior. The paper focuses on the time variance of the capacitor behavior, which is exemplified in the case of a polymer electrolytic capacitor. We performed the study on a C-R model considering that, during the discharge transient process, both parameters are time-variant. To prove this, we use two types of experimental data: data measured during the capacitor’s discharge process and data obtained from frequency characteristics of ESR and C of the capacitor. Next, the article proposes an estimation method of equivalent values for the model parameters C and R based on the time variance highlighted by the experimental data. The estimation method uses a system of equations associated with the discharging of capacitors, respectively, to the frequency characteristics via polynomial regression. We developed an estimation procedure in two variants, which differ by the sets of measured points taken on the discharge characteristic. The experiments were carried out with an electrolytic polymer capacitor rated 220 µF, 25 V, 2.5 A rms, 85 ℃, designed mainly for energy storage and filtering, the results being confirmed by experiments performed on other similar capacitors. The subject of the paper is part of a research topic aimed at monitoring the health status of capacitors as key components with high breakdown rates in power electronics.

#### Numerical solution of the classic Ekman Model considering variable Eddy Viscocity profile and bottom boundary layer

Viviana Santander Rodriguez1

1Escuela Superior Politécnica del Litoral, Facultad de Ingeniería Marítima y Ciencias del Mar, Ecuador

###### Abstract

The action of the wind on the sea surface as a result of the wind blowing yields internal friction, i.e., turbulence. The upper ocean layer acts as a gearing mechanism that transmits motions to deeper levels. When the wind force moves surface water, it takes the following layers of water as well. Each layer of water moves by friction more slowly than the upper layer until the movement ceases at depth. However, like surface waters, deeper waters are deflected by the Coriolis effect. The classical Model of Ekman proposes a hypothetical ocean, including the influence of continents, Coriolis forces, and assuming a constant vertical eddy viscosity. The range of the turbulence mixing carries variations of the eddy viscosity, and this parameter depends on how well stratified the water column is. This study considers that among the parameters involved in the transfer of momentum, the internal friction due to wind stress on the sea surface and the eddy viscosity in the water column are relevant. Using numerical methods, the momentum equations for the $x$ and $z$ components were solved for a turbulent, homogeneous and inhomogeneous boundary layer, at steady state in a finite water column. $$fv+\ k_z(z)\ \frac{\partial^2u}{{\partial z}^2}\ =\ 0$$ $$-fu\ +\ k_z(z)\ \frac{\partial^2v}{{\partial z}^2}\ =\ 0$$ Using ordinary differential equation techniques with surface $z = 0$ and bottom $z = h$ boundary conditions: $$\rho k_z\left(z\right)\left.\frac{\partial u}{\partial z}\right|z=0 = Txz$$ $$\rho k_z\left(z\right)\left.\frac{\partial v}{\partial z}\right|z=0 = 0$$ $$u(-h) = 0$$ $$v(-h) =0$$ Where $Txz$ represents the wind shear stress. Although the classical Ekman model considers the turbulent viscosity coefficient, $kz$, as a constant, in this study this coefficient is expressed as a function of the depth levels at which changes in its profile occur and the value of $kz$ on the surface. A depth understanding of the eddy viscosity coefficient along the water column that results from the density variation with depth is helpful to obtain a more realistic behavior compared to the Ekman classical model. Resulting in smaller deviation angles for a stratified water column, and with variable turbulent viscosity coefficient, in turn, towards greater depths the deviation angle tends to $70 °$.

###### Acknowledgements:

The author kindly acknowledge the financial support from ESPOL.

#### Monte Carlo studies on shape deformation and stability of 3D skyrmion under mechanical stresses

Hiroshi Koibuchi1 , Satoshi Hongo2 , Fumitake Kato3 , Gildas Diguet4 , Tetsuya Uchimoto5 , Sahbi Hog6 , Hung Diep7

1National Institute of Technology (KOSEN), Sendai College, , Japan
2National Institute of Technology, Sendai College (Kosen), , Japan
3National Institute of Technology, Ibaraki College (Kosen), , Japan
4Institute of Fluid Science, Tohoku University, , Japan
5Institute of Fluid Science, Tohoku University, , Japan
6University of Monastir, , Tunisia
7CY Cergy Paris University, , France

###### Abstract

H. Koibuchi1), S. Hongo1), F. Kato2), S. El Hog 3) , G. Diguet4,5), T. Uchimoto4,5) and H.T. Diep6) 1)National Institute of Technology (KOSEN), Sendai College, Natori, Japan. 2)National Institute of Technology (KOSEN), Ibaraki College, Hitachinaka, Japan. 3)Universite de Monastir (LMCN), Monastir, Tunisie 4)Institute of Fluid Science (IFS), Tohoku University, Sendai, Japan 5)ElyTMax, CNRS-Universite de Lyon-Tohoku University, Sendai, Japan 6) CY Cergy Paris University, Cergy-Pontoise, France Skyrmions are topologically stable spin configurations in chiral magnets and attract much attention for future spintronics devices. Recent experimental studies indicate that mechanical stresses play a non-trivial role in deforming skyrmion (sky) configurations. The sky shape deforms under uniaxial tensile stress, and it is also stabilized/destabilized by uniaxial stresses depending on whether the stress is tensile or compressive. The authors recently study the sky deformation by Monte Carlo simulations on triangular lattices and conclude that the deformation attributes to anisotropy in Dyaloshinskii-Moriya interaction (DMI), where a strain field is introduced as a non-polar variable to implement magneto-elastic effects via Finsler geometry (FG) modeling technique (DOI: 10.1103/PhysRevB.104.024402). In this study, we extend this model to a 3D model on tetrahedral lattices. In 3-dimensional materials, the strain field has values on the half sphere, and hence, non-trivial interaction with electronic spins, which have values on the unit sphere, is expected. We find that the same conclusion is obtained in the 3D model as in the 2D model for sky deformation such that DMI anisotropy is the origin of the deformation. Moreover, DMI anisotropy in the 3D model is also considered to be an origin of stabilization/destabilization of sky. This implies that a proper mechanism for the stabilization/destabilization of sky is implemented in the 3D FG model as a magneto-elastic effect in chiral magnetic materials.

###### Acknowledgements:

This work is supported in part by the Collaborative Research Project of the Institute of Fluid Science, Tohoku University, and JSPS KAKENHI 20H04647.

#### Mean-field parameters of some $Pr_{x}Tb_{(1-x)}Al_{2}$ compounds found via searching for the best magnetic heat capacity fitting

Julio Tedesco1 , Vagner Monteiro2 , Alexandre Magnus de Carvalho3 , Lisandro Cardoso4 , Adelino Coelho5

1Polytechnique Institute of Rio de Janeiro State University (IPRJ/UERJ), Mechanics and Energy Department, Brazil
2Polytechnique Institute of Rio de Janeiro State University (IPRJ/UERJ), Engineering Mechanics and Energy Department, Brazil
4Institute of Physics “Gleb Wataghin” – IFGW, State University of Campinas, Applied Physics Department, Brazil
5Institute of Physics “Gleb Wataghin” – IFGW, State University of Campinas, Applied Physics Department, Brazil

###### Abstract

Simulations of the magnetic heat capacity of some $(Pr,Tb)Al_2$ compounds were performed using the mean-field approach. The developed routine aims to optimize the set of mean-field parameters. The proposed algorithm calculates the sum of squared differences between the experimental points and the simulated curve and then changes the parameters in order to minimize this sum. This searching leads to consistent values that can reproduce the experimental data. The parameters found in this work reproduced the heat capacities curves of the $Pr_{x}Tb_{(1-x)}Al_{2}$ compounds, $x=0.25$, $x=0.50$ and $x=0.75$, with good agreement. The physical limitations of the mean-field approach do not preclude analysing the results. These parameters are important because they can help to understand and calculate the magnetocaloric effect these materials can present.

#### Attempt to quantify the impact of seasonal air density variation on operating tip-speed ratio of small wind turbines

Hiroki Suzuki1 , Yutaka Hasegawa2 , Oluwasola Afolabi3 , Shinsuke Mochizuki4

1Okayama University, Graduate School of Natural Science and Technology, Japan
2Nagoya Institute of Technology, Department of Electrical and Mechanical Engineering, Japan
3Loughborough University, School of Architecture, Building and Civil Engineering, United Kingdom
4Yamaguchi University, Graduate School of Sciences and Technology for Innovation, Japan

###### Abstract

This study presents the impact of seasonal variation in air density on the operating tip-speed ratio of small wind turbines. The air density, which varies depending on the temperature, atmospheric pressure, and relative humidity, has an amplitude of about 5% in Tokyo, Japan, annually. This study attempts to quantify this impact by using the equation of motion of the rotational speed in a small wind turbine shown by previous work. This governing equation has been simplified by expanding a profile of the aerodynamic torque coefficient for a wind turbine rotor to the tip-speed ratio. Moreover, this governing equation is simplified in this study by using non-dimensional forms of the air density, inflow wind velocity, and rotational speed with these characteristic values. In this study, the load of a generator is set to be constant based on a previous analysis of a small wind turbine. By considering the equilibrium between the aerodynamic torque and the load torque of the governing equation at the optimum tip-speed ratio, the impact of the variation in the air density on the operating tip-speed ratio can be expressed using a simple mathematical form. As shown in this derived form, the operating tip-speed ratio is found to be less sensitive to a variation in air density than that in inflow wind velocity.

#### Impact of difference between explicit and implicit second-order time integration schemes on isotropic/anisotropic steady incompressible turbulence field

Ryuma Honda1 , 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 effect of the conservation error of kinetic energy on the turbulence fields. The present study uses the Reynolds number dependence of the steady turbulence given by an external forcing term that sets the large-scale turbulence field isotropically or anisotropically. When the conservation of the kinetic energy of the scheme used for the analysis is explicit, if the time integration method is implicit, the accuracy of the conservation of the kinetic energy can be decreased. In this study, the conservation error of the kinetic energy is produced using the second-order Crank-Nicholson method, which is a standard implicit method. For the case where there is the negligible conservative error, the governing equation is integrated for the time using the second-order Adams-Bashforth method, an explicit method. The observed effects of the conservation error are obtained using turbulence statistics and visualization results.

#### A layer potential approach to functional and clinical brain imaging

Paul Asensio1 , Jean-Michel Badier2 , Juliette Leblond3 , Jean-Paul Marmorat4 , Masimba Nemaire5

1Inria, FACTAS, France
2 Aix-Marseille Université, , France
3Inria, FACTAS, France
4Mines Paristech (Sophia Antipolis), , France
5Inria, FACTAS, France

###### Abstract

In this work we consider the inverse source recovery problem from sEEG, EEG and MEG point-wise data. We regard this as an inverse source recovery problem for $L^2$ vector-fields normally oriented and supported on the grey/white matter interface, which together with the brain, skull and scalp form a non-homogeneous layered conductor. We assume that the quasi-static approximation of Maxwell's equation holds for the electro-magnetic fields considered. The electric data is measured point-wise inside and outside the conductor while the magnetic data is measured only point-wise outside the conductor. This ill posed problem is solved via Tikhonov regularization on triangulations of the interfaces and a piecewise linear model for the current on the triangles. Both in the continuous and discrete formulation the electric potential is expressed as a linear combination of double layer potentials while the magnetic flux density in the continuous case is a vector-surface integral whose discrete formulation features single layer potentials. A main feature of our approach is that these contributions can be computed exactly. Due to the consideration of the regularity conditions of the electric potential in the inverse source recovery problem, the Cauchy transmission problem for the electric potential is inadvertently solved as well. In this Cauchy transmission problem for the electric potential we propagate only the electric potential while the normal derivatives at the interfaces of discontinuity of the electric conductivities are computed directly from the resulting solution. This reduces the computational complexity of the problem. Because of the connection between the magnetic flux density and the electrical potential in conductors such as the one we explore, a coupling of the sEEG, EEG and MEG data for solving the respective inverse source recovery problems simultaneously is direct. We treat these problems in a unified approach that uses only single and/or double layer potentials. We provide numerical examples using realistic meshes of the head with synthetic data.

#### On Multiquadric Shape Determining Strategies in Image Reconstruction Applications: A Comparative Study

Sayan Kaennakham1

1Suranaree University of Technology, School of Mathematiccs , Thailand

###### Abstract

After being introduced to approximate two-dimensional geographical surfaces in 1971, the multivariate radial basis functions (RBFs) have been receiving a great amount of attention from scientists and engineers. Over decades, RBFs have been applied to a wide variety of problems. Approximation, interpolation, classification, prediction, and neural networks are inevitable in nowadays science, engineering, and medicine. Moreover, numerically solving partial differential equations (PDEs) is also a powerful branch of RBFs under the name of the ‘Meshfree/Meshless’ method. Amongst many, the so-called ‘Multiquadric (MQ)’ is known as one of the mostly used forms of RBFs. It is of $\sqrt{\epsilon^2+r^2}$ form where $r$ represents the Euclidean distance function. The key factor playing a very crucial role for MQ, or other forms of RBFs, is the so-called ‘shape parameter, $\epsilon$ ’ where selecting a good one remains an open problem until now. This paper focuses on measuring the numerical effectiveness of various choices of $\epsilon$ proposed in literature when used in image reconstruction problems. Condition number of the interpolation matrix, CPU-time and storage, and accuracy are common criteria being utilized. The results of the work shall provide useful information on selecting a ‘suitable and reliable choice of MQ-shape’ for further applications in many branches.

#### Group classification of the generalized Klein-Gordon equation by the method of indeterminates

Jean-Claude Ndogmo1

1University of Venda, Mathematics and Applied mathematics, South Africa

###### Abstract

A method for the group classification of differential equation we recently proposed is applied to the classification of the generalized Klein-Gordon equation that arises in mathematical physics. Our results are compared with other classification results of this family of equations labelled by an arbitrary function which may be seen as the derivative of a potential function. Some conclusions are drawn about the effectiveness of the proposed method.

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

Giorgio Frunzio1 , Luciana Di Gennaro2

1Università degli Studi della Campania Luigi Vanvitelli, Architecture and Industrial Design, Italy
2Università degli Studi della Campania Luigi Vanvitelli, Engineering, 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 behavior of structures in term 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. 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 framework reinforced concrete structure has been based on the experimental data obtained by a scaled model. The simplified method proposed consists in 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.

#### Out‑of‑plane behaviour of masonry infills

Giorgio Frunzio1 , Luciana Di Gennaro2

1Università degli Studi della Campania Luigi Vanvitelli, Architecture and Industrial Design, Italy
2Università degli Studi della Campania Luigi Vanvitelli, Engineering, Italy

###### Abstract

The serious damage observed in recent earthquakes confirmed the high vulnerability of masonry infills inside reinforced concrete (RC) frames under out-of-plane load. Their damage causes consequences in terms of life losses and repair or reconstruction costs, so the behavior these elements has become a topic of great interest today. The infills are usually considered as non-structural elements, while their presence can often considered a structural behavior enhancement of the reinforced concrete frame. Several numerical models have been proposed to evaluate infilled elements, but limited experimental data have been used to validate the models. This paper considers simplified out-of-plane collapse mechanisms, taking into account the connections with the floor and the transverse walls, to evaluate the behavior of masonry walls subject to out-of-plane forces. In general, the walls can be represented as an equivalent SDOF system, in order to evaluate the horizontal limit force at the oscillation threshold by simple static analysis, assuming that the link at the base of the infill is cracked and therefore the traction and the strength of the mortar can be neglected. Similarly, from that simple kinematic model the displacement at the tipping threshold is derived. Validation with literature experimental data is proposed.

###### Acknowledgements:

The authors gratefully acknowledge the University of Campania for the financial support

#### Group analysis and conservation laws of a fourth order wave equation

Jean-Claude Ndogmo1

1University of Venda, Mathematics and Applied mathematics, South Africa

###### Abstract

We consider a fourth order Lagrange wave equation and investigate its low order conservation laws. Using a combination of Noether theorem and a direct method, we find all conservation laws of the equation not exceeding the second order. Variational and divergence symmetries of the equation are also classified. This yields in particular a reduction in order of the equation for which some soliton solutions are derived.

#### Weather in field artillery ballistics calculation

Marian Mendel1

1Military Institute of Armament Technology, Ballistcs Department, Poland

###### Abstract

The most important meteorological data are: ambient temperature, precipitation quantity, air humidity, amount and type of clouds, atmospheric pressure, wind direction and speed, visibility, weather phenomena. These coefficients impact the effectiveness of various activities, especially those conducted in an open space. Knowledge of future weather conditions is essential for planning the area of operations, calculating times, choice of means, and other aspects relevant to the upcoming tasks. Taking weather conditions into account is vital, specifically when it comes to planning combat operations, where cooperation accuracy is of paramount importance. Rocket forces and artillery are one particular type of armed forces where weather conditions are critical. The effectiveness of artillery depends on the precision of ballistic calculations, and so knowledge of atmospheric conditions is fundamental. Atmospheric data are collected from sounding, using a probe attached to a balloon. It is commonly known that particular meteorological parameters change in a spatial smooth manner, depending on various coefficients. The information about the atmosphere collected from a single sounding may be insufficient, due to the possibility of a balloon drifting away from the area of interest, and the calculations are based on data received from the sounding. In this paper, I will suggest a method for preparing artillery use meteorologically, which takes into account the distribution of particular meteorological coefficients over a given area, such as the field of operations over which potential trajectories of shells and rockets will be located. The data are collected from: ground meteorological stations, satellite imagery, radar imagery, outcomes of lightning activity detection, vertical sounding of atmosphere.

#### Mapping energy spectra of Coulomb interacting bi-particle systems using multi-target regression methods

George Alexandru Nemnes1 , Tudor Luca Mitran2 , Dragos-Victor Anghel3 , Amanda Teodora Preda4 , Iulia Ghiu5 , Virgil Baran6 , Mihai Marciu7 , Andrei Manolescu8

1Research Institute of the University of Bucharest (ICUB), , Romania
2Research Institute of the University of Bucharest (ICUB), , Romania
3Research Institute of the University of Bucharest (ICUB), , Romania
4Research Institute of the University of Bucharest (ICUB), , Romania
5Research Institute of the University of Bucharest (ICUB), , Romania
6Research Institute of the University of Bucharest (ICUB), , Romania
7University of Bucharest, Faculty of Physics, , Romania
8Department of Engineering, Reykjavik University, , Iceland

###### Abstract

The continuous downscale of electronic devices is motivated by higher switching speeds and packing densities, while new quantum computing architectures have been proposed, which rely on the ability to maintain the wavefunction coherence and perform operations onto the quantum many-body states. Quantum dot arrays implemented as cross-bar schemes [1,2] have been experimentally investigated as prototypes which can integrate a large number of q-bits. Understanding the operation of multi-electron devices requires a significant computational effort due to the complexity of the many-body wavefunction. In many cases, the few-electron quantum system of interest is required to be investigated for multiple input conditions, which results in a large set of systems with overlapping properties. Here, we consider a two-dimensional finite 2-electron system, with an array of N x N top gates, which controls the electrostatic potential below, in the active region. The voltage corresponding to each gate can be individually set by one of the two possible values, labeled as low and high voltage, yielding an exponential number of potential configurations. The energy spectra are obtained using the exact diagonalization method (EDM) from the many-body Hamiltonian [3]. Solving exhaustively the set of systems by EDM becomes prohibitive even for a moderate number of gates while, in addition, the Coulomb interaction can be tuned by the underlying materials. Therefore, we investigate in how far a mapping between energy spectra of random subsets of non-interacting systems and interacting systems can be accurately achieved. To this end, we employ multi-target regression methods, e.g. based on artificial neural networks. This approach provides a significant reduction of the computational burden for a large set of many-body systems within a given class. References: [1] Ruoyu Li, Luca Petit, David P. Franke et al., Science Advances 7, (2018); [2] N. Lee, R. Tsuchiya, G. Shinkai et al., Appl. Phys. Lett. 116, 162106 (2020); [3] V. Moldoveanu, A. Manolescu, Chi-Shung Tang et al., Phys. Rev. B 81, 155442 (2010).

###### Acknowledgements:

This work was supported by a grant of the Romanian Ministry of Research, Innovation and Digitalization, CNCS - UEFISCDI, project number PN-III-P4-ID-PCE-2020-1142, within PNCDI III.

#### Solving bio-heat transfer multi-layer equation using Green's Functions method

EDUARDO PEIXOTO DE OLIVEIRA1 , Gilmar Guimarães2

###### Abstract

An analytical method using Green's Functions for obtaining solutions in bio-heat transfer problems, modeled by Pennes' Equation, is presented. Mathematical background on how treating Pennes' equation and its $\mu^2$T term is shown, and two contributions to the classical numbering system in heat conduction are proposed: inclusion of terms to specify the presence of the fin term, $\mu^2$T, and identify the biological heat transfer problem. The presentation of the solution is made for a general multi-layer domain, deriving and showing general approaches and Green's Functions for such n number of layers. Numerical examples are presented to simplify human skin as a two-layer domain: dermis and epidermis, accounting metabolism as a heat source, and blood perfusion only at the dermis. Time-independent summations in the series-solution are written in closed forms, leading to better convergence along the boundaries. Details on obtaining the two-layer solution and its eigenvalues are presented for boundary conditions of prescribed temperature inside the body and convection at the surface, such as its intrinsic verification.

#### Quantized toroidal dipole eigenvalues in nano-systems

Amanda Teodora Preda1 , Dragos-Victor Anghel2

1Research Institute of the University of Bucharest (ICUB), , Romania
2Horia Hulubei National Institute for R&D in Physics and Nuclear Engineering, Department of Theoretical Physics, Romania

###### Abstract

The parity violation in nuclear reactions led to the discovery of the new class of toroidal multipoles. Since then, it was observed that toroidal multipoles are present in the electromagnetic structure of systems at all scales, from elementary particles, to solid state systems and metamaterials. The toroidal dipole $\textbf{T}$ (the toroidal multipole of the lowest order) is the most common. This corresponds to the toroidal dipole operator $\hat{\textbf{T}}$ in quantum systems, with the projections $\hat{T}_i$ ($i=1,2,3$) on the coordinate axes. These operators are observables if they are self-adjoint, but, although it is commonly discussed of toroidal dipoles in both classical and quantum systems, up to now no system has been identified in which the operators are self-adjoint. Therefore, in this paper we use what are called the natural coordinates'' of the $\hat{T}_3$ operator to give a general procedure to construct operators that commute with $\hat{T}_3$. Using this method, we introduce the operators $\hat{p}^{(k)}$, $\hat{p}^{(k1)}$, and $\hat{p}^{(k2)}$, which, together with $\hat{T}_3$ and $\hat{L}_3$, form two complete systems of compatible observables: $(\hat{p}^{(k)}, \hat{T}_3, \hat{L}_3)$ and $(\hat{p}^{(k1)}, \hat{p}^{(k2)}, \hat{T}_3)$. Using the set $(\hat{p}^{(k)}, \hat{T}_3, \hat{L}_3)$ and the `natural coordinates'', we propose a system geometry and an operator $\hat{\tilde{T}}_3$, composed of $\hat{p}^{(k)}$, $\hat{T}_3$, and $-\hat{p}^{(k)}$, which is self-adjoint and, therefore, an observable. Moreover, in the proposed geometry, the eigenfunctions $\hat{\tilde{T}}_3$, which are common to those of $\hat{T}_3$, are quantized. Such systems open up the possibility of making metamaterials which exploit the quantization and the quantum properties, in general, of the toroidal dipoles.

###### Acknowledgements:

This work has been financially supported by UEFISCDI project PN-19060101/2019 and the ELI-RO contract 81-44 /2020.

#### Power law distributions in a new toy model with interacting $N$ agents

Tohru Tashiro1

1Aichi University of Technology, Comprehensive Education Center, Japan

###### Abstract

Various phenomena, where the observed value of a quantity, or the size of the observation, is proportional to a power of the "rank" of the observation, ubiquitously occur in nature. In particular, if the exponent is close to -1, the rank–size distribution is called Zipf's law which we can find in a wide range of fields, e.g., magnitudes of earthquakes, populations of cities, and incomes of companies. We can show that the empirical law corresponds to a power law distribution whose exponent is -2. The fact that the power law distribution can be found in such a diverse field indicates the presence of a common mechanism behind the universality. However, there are few researches approaching it. In this presentation, I would like to introduce a new toy model with interacting $N$ agents. The agents in the model posses a quantity and an interacting radius depending the quantity. I will show that the distribution of the quantity of the agents is given by the power law in a steady state after the many interactions.

#### Photoacoustic spectroscopy allows to make correlations between blood p450 cytochrome and glycemia type 1 experimental diabetes

Lilia Ivonne Olvera Cano1 , Guadalupe Villanueva López2 , Evelyn Romero Mateos3 , Alfredo Cruz Orea4

1Escuela Superior de Física y Matemáticas del Instituto Politécnico Nacional, Physics, Mexico
2Escuela Superior de Medica del Instituto Politécnico Nacional, , Mexico
3Escuela Superior de Medica del Instituto Politécnico Nacional, , Mexico
4Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Physics, Mexico

###### Abstract

In 2019, 463 million people were affected by diabetes, which is the second cause of death in Mexico. Patients with diabetes die because of the long-term complications. Early detection of those complications is difficult. In previous work, we have observed that photoacoustic spectrometry, a nondestructive technique is applicable on measurements of glycemia and other components in small blood samples. The goal of the study was to apply the phase-resolved method to make a time-course study of components of blood in experimental type 1 diabetes. Diabetes was produced in male Wistar rats through the administrations of streptozotocin (STZ). A group treated with STZ vehicle was used as control. Blood samples were taken weekly from the tail of rats for 10 weeks and submitted to photoacoustic spectroscopy. The phase-resolved method allowed to detect p450 cytochrome in blood. There was a significant and positive correlation between glycemia and p450 cytochrome (p=0.001). Since p450 participates in detoxification function, results indicate that blood glucose could affect the management of toxics. It will be important, in future studies, to study the implications of those results on the development of diabetes complications. The novelty of the study was to use photoacoustic spectroscopy to study different components of blood in experimental type 1 diabetes in order to detect changes produced by glycemia, which will eventually will help to the early detection of diabetes complications.

#### Prediction of the microstructural grain evolution during selective laser melting by a cellular automata method

Lin Wang1

1Hefei University, Department of Civil Engineering, China

###### Abstract

The mechanical properties of additively fabricated metallic parts are closely correlated with their microstructural texture. Knowledge about the grain evolution phenomena during the additive manufacturing process is of essential importance to accurately control the final structural material properties. In this work, a two-dimensional model based on the cellular automata method was developed to predict the grain evolution in the selective laser melting process. The effectiveness of this presented model is proven by comparing the simulated and reported results. The influence of process parameters, like the heat power, scanning speed, and patterns, on the microstructural grain morphology are numerically evaluated.

#### General properties of exchange rate of national money versus some foreign currencies in Albania

Sandër Kovaçi1 , Agron Gjana2

1Polytechnic University of Tirana, Department of Mathematical Engineering, Albania
2Polytechnic University of Tirana, Department of Mathematical Engineerin, Albania

###### Abstract

In this work we have considered the study of the exchange rate series for the specific case where the formal financial market is not active. In those situations, we would be interested in the parallelization of the exchange rate with financial indexes for stabilized financial market. We observed that the stationarity of the distribution for some the exchange rate of currencies traded in the country differs significantly. The time dynamics shows the presence of the elements of local critical behavior, but those tendencies attenuate and fade away in an aperiodic fashion. Next, we considered and evidenced the correlation distances and dissimilarity between exchange rates of national currencies versus euro and dollar and golden prices. It resulted that two exchange rates do have different distance from golden price taken for references. The correlation distance between the series of the returnin different period has evidenced that there is not a regular behavior in this respect.

#### On the distribution of the atomic planes in an elastic single-crystal bar under the action of volumetric forces

Леонид Карыев1

1Derzhavin Tambov State University, Tambov district, Russian Federation

###### Abstract

L.G. Karyev*, V.A.Fedorov, A.D. Berezner Derzhavin Tambov State University, Russia *karyev@list.ru The paper presents a theoretical study of the behaviour of atomic planes in an elastic single-crystal bar under conditions of the action of volumetric forces on it - inertia and gravity. The forces are directed along the axis of the bar where the x-axis is located. Within the framework of the linear theory of elasticity, the function γ (x) is the linear density of the atomic planes that are perpendicular to the x-axis in the bar, and this function is obtained by comparison between discrete and continuous. In the concept of this regularity, the functions δ (x) and ε (x) (longitudinal stress and relative deformation, respectively) are not linear. Since the elastic forces are electromagnetic and are largely determined by electrostatic interaction, the found regularity will describe the distribution law of uniformly charged ionic planes in a metal single-crystal bar (accurate to coefficients) under the conditions of an external a uniform electric field, wherein the force lines are directed along the bar. The action of a volumetric electrostatic force is of independent interest. Moreover, knowledge of such a pattern would be useful in studying the behaviour of a complex of like-charged plates, for example, membranes located in an electric field and oriented relative to each other like atomic planes in a single crystal.

#### Development of a Quantum Mechanical Autoencoder Model

1Aarhus University, Department of Physics and Astronomy, Denmark

###### Abstract

An auto encoder is a type of artificial neural network, which efficiently learns to replicate a set of data values. These values are unlabeled, so that the learning process is effectively unsupervised. The auto encoder is modelled by an encoding-decoding scheme, along with the option of internal compression. Data compression is a useful tool for simplifying distribution detail, so it can assist the auto encoder in optimizing a more vauge representation of the learned distributions. Some amount of internal compression can be necessary to efficiently learn a set of data values. \\ Advantages in machine learning have recently (2018) been investigated in quantum mechanical qubit systems by \lbrack Havlíček et al.\rbrack\ among others. In continuation of their research, another group \lbrack Abbas et al.\rbrack\ formulated two definite feature maps to formulate an effective quantum neural network. One an input feature map $\mathcal{U}(\vec{x})$ depending on an input vector $\vec{x}\in \mathbb{R}^s$ of a circuit of $s$ qubits. The other, a variational map $\mathcal{G}(\vec{\theta})$ depending on parameters $\vec{\theta}$, which may be varied. With these building blocks and a method of internal circuit compression formulated by \lbrack Romero et. al.\rbrack, my bachelor project sought to mathematically engineer and simulate a quantum mechanical autoencoder model. A definite model of this type has previously not been avaliable, and this project introduces and tests a quantum circuit which has the properties of the classical auto encoder model. The tested model is given by a consecutive use of feature maps: $$\mathcal{M}^\dagger(\vec{x})\cdot \mathcal{G}^\dagger(\vec{\theta}_d) \cdot\hat{R}\cdot\hat{C}\cdot\mathcal{G}(\vec{\theta}_e)\cdot\mathcal{U}(\vec{x})|0 \rangle ^{\otimes s}$$ As the circuit size $s$ and network depth $d$ increases, the number of singular quantum logic gates scales by the polynimial $2s^2 + (2d+5)s$. Internal compression is acquired by measuring a set of qubits ($\hat{C}$) and instantly replacing them by the $|0\rangle$ basis state ($\hat{R}$). The feature map $\mathcal{M}(\vec{x})$ is applied last and acts as a mimic to the input feature map $\mathcal{U}$. The mimic $\mathcal{M}$ is formulated so that the input vector $\vec{x}$ can be reconstructed by the circuit output $\mathcal{M}(\vec{x})|0 \rangle ^{\otimes s}$. Specifically, the map is defined by a set of seperable qubits $|x_i\rangle = R_y(x_i) \hat{H}|0\rangle$ for each $x_i\in \vec{x}$. Here $R_y$ is the $y$-rotation matrix and $\hat{H}$ is the Hadamard gate. The input vector can be reconstructed by repeated measurements of of the qubits, with the formula $$\notag x_i = 2\arctan\left(\sqrt{\Gamma_i}\right) - \frac{\pi}{2}.$$ Where $\Gamma_i = |\alpha_i|^2 / |\beta_i|^2$ is defined to be the qubit ratio probability of a general qubit $|\psi\rangle = \alpha|0\rangle + \beta|1\rangle$. The circuit of the quantum mechanical auto encoder is simluated using the QuTiP python package. \\ A relatively large fidelity measure was acquired with the developed model, through testing on the Iris data set; A mean fidelity topping at $97.57\%$ for an QAE model with a depth of 4 and compression 1. The Fischer information spectrum has been calculated for QAE models of varying amount of compression. The spectrum has considerably more large Fischer eigenvalues than that simulated by \lbrack Karakida et al.\rbrack\ on a classical auto encoder model. Graphs of training processes, input reconstruction and Fischer eigenvalues has been constructed. \newpage References: \begin{itemize}[label=$-$] \item \lbrack Abbas et al.\rbrack\ A. Abbas, D. Sutter, C. Zoufal, A. Lucchi, A. Figalli and S. Woerner: "The power of quantum neural networks (2020)", at \url{https://arxiv.org/abs/2011.00027} \item \lbrack Havlíček et al.\rbrack\ V. Havlíček and A. D. Córcoles and K. Temme and A. W. Harrow and A. Kandala and J. M. Chow: "Supervised learning with quantum-enhanced feature spaces (2019)", at DOI: 10.1038/s41586-019-0980-2 \item \lbrack Karakida et al.\rbrack\ R. Karakida and S. Akaho and S. Amariat : "Universal Statistics of Fisher Information in Deep Neural Networks: Mean Field Approach (2018).", at \url{https://arxiv.org/abs/1806.01316} \item \lbrack Romero et al.\rbrack\ J. Romero, J. P. Olsen, A. Aspuru-Guzik: "Quantum autoencoders for efficient compression of quantum data (2017)", at \url{https://arxiv.org/abs/1612.02806} \end{itemize}

###### Acknowledgements:

Prof. Nikolaj T. Zinner

#### THE INFLUENCE OF JOINT GEOMETRY OF TONEHOLES WITH THE MAIN BORE OF WIND MUSICAL INSTRUMENTS ON THEIR FREQUENCY CHARACTERISTICS

Roman Gerasimov1

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

###### Abstract

The article discusses the influence of geometric parameters (the presence and magnitude of the radius of curvature) at the junction of the toneholes with the main bore of the air column on the frequency characteristics of wind musical instruments. A theoretical calculation of the eigenfrequencies of an air column with one tonehole in the case of sharp edges has been carried out. The resonance frequencies were also found using computer simulation in the COMSOL Multiphysics 5.5 program for the case of sharp edges and joints with a radius of curvature. An empirical dependence of the frequency of the main tone of the air column on the radius of curvature of the edges of the tonehole is obtained. All calculations were carried out for two models: without and taking into account viscous drag and thermal exchange losses.

#### Retweets’ time series analysis using wavelet methods

Andrey Dmitriev1 , Vasily Kornilov2 , Victor Dmitriev3 , Elizaveta Petyaeva4

1National Research University Higher School of Economics, Business Informatics, Russian Federation
2National Research University Higher School of Economics, Business Informatics, Russian Federation
3National Research University Higher School of Economics, Business Informatics, Russian Federation
4National Research University Higher School of Economics, Business Informatics, Russian Federation

###### Abstract

Recently, there has been numerous evidence of the existence of self-organized critical (SOC) transitions in various online social networks (OSN), including Twitter, and various sociophysical models of SOC transitions have been proposed. Despite this, some problems remained unresolved, for example, those related to the determination of the spectral featers of subcritical and supercritical phases of the information stochastic dynamics aggregated by OSNs. We obtained a time series of the retweets number corresponding to three 2016 United States Presidential Election debates. Next, we performed multifractal analysis of the time series using the wavelet leader method and scalograms analysis for continuous wavelet transform of the time series. Multifractal analysis is needed because scaling exponents for the time series are the nonlinear functions of the moments. It was found that the frequency of stochastic oscillations of retweets corresponds to 1/f noise and is the highest during the first, second and third debates. In the time intervals preceding and following the debate, the oscillation frequencies are reduced to the values ​​approximately corresponding to white noise. As we approach to the start of the debate, there is an increase in the magnitude and frequency of the retweets ’oscillations.

###### Acknowledgements:

This work was partially funded by the Russian Foundation for Basic Research (Grant no. 20-07-00651). 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).

#### Cosmological model with non-minimally coupled $k$-essence

Kairat Myrzakulov1 , Yerlan Myrzakulov2 , Gulmira Yergaliyeva3

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

###### Abstract

This paper is devoted to study some model of $k$-essence in the homogeneous and isotropic Universe, where the scalar field non-minimally coupled to gravity. Using the variational method, we obtained the corresponding system of field equations, and we found their particular solutions for the coupling function $f(\phi)$, the form of the function of the non-canonical kinetic term $K(X)$ and the potential of scalar field $V(\phi)$. Finally, we substituting these particular solutions into the field equations, we obtained equations that depend only on the scale factor $a(t)$ and the scalar field $\phi$. We obtained cosmological solutions show that our model can be used to describe the dynamics of the Universe.

###### Acknowledgements:

This work was supported by the Ministry of Education and Science of Kazakhstan under grants AP08052034.

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

Kairat Myrzakulov1 , Yerlan Myrzakulov2 , Sabit Bekov3

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

###### Abstract

In this work, we considered homogeneous and isotropic cosmological model of the Universe in $f(T,B)$ gravity with non-minimally coupled fermionic field. In order to find the form of the coupling function $F(\Psi)$, the potential function $V(\Psi)$ of the fermionic field and the function $f(T,B)$, we used the Noether symmetry approach. The results obtained are coincide with the observational data that describe the late-time accelerated expansion of the Universe.

###### Acknowledgements:

This work was supported by the Ministry of Education and Science of Kazakhstan under grants AP08052034.

#### Does the Zero Carry Essential Information for Artificial Neural Network learning to simulate the contaminant transport in Urban Areas?

Monika Berendt-Marchel1 , Anna Wawrzynczak2

1Siedlce University of Natural Sciences and Humanities, Institute of Computer Sciences, Poland
2Siedlce University of Natural Sciences and Humanities, Institute of Computer Sciences, Poland

###### Abstract

The release of hazardous materials in urbanized areas is a considerable threat to human health and the environment. Therefore, it is vital to detect the contamination source quickly to limit the damage. In systems localizing the contamination source based on the measured concentrations, the dispersion models are used to compare the simulated and registered point concentrations. These models are run tens of thousands of times to find their parameters giving the best fit of the model output to the registration. Artificial Neural Networks (ANN) can replace in localization systems the dispersion models, but first, they need to be trained on a large, diverse set of data. However, providing an ANN with a fully informative training data set leads to some computational challenges. For example, a single simulation of airborne toxin dispersion in an urban area might contain over 90% of zero concentration in the positions of the sensors. This leads to the situation when the ANN target includes a few percent positive values and many zeros. As a result, the neural network focuses on the more significant part of the set - zeros, leading to the non-adaptation of the neural network to the studied problem. Furthermore, considering the zero value of concentration in the training data set, we have to face many questions: how to include zero, how to scale a given interval to hide the zero in the set, and include zero values at all; or to limit their number? This paper will try to answer the above questions and investigate to what extend zero carries essential information for the ANN in the contamination dispersion simulation in urban areas. For this purpose, as a testing domain, the center of London is used as in the DAPPLE experiment. Training data is generated by the Quick Urban & Industrial Complex (QUIC) Dispersion Modeling System.

#### Hybrid modeling of the human cardiovascular system using NeuralFMUs

Tobias Thummerer1 , Johannes Tintenherr2 , Lars Mikelsons3

1Augsburg University, Chair of Mechatronics, Germany
2Augsburg University, , Germany
3Augsburg University, , Germany

###### Abstract

Hybrid modeling, the combination of first principle and machine learning models, is an emerging research field that gathers more and more attention. Even if hybrid models produce formidable results for academic examples, there are still different technical challenges that hinder the use of hybrid modeling in real-world applications. By presenting NeuralFMUs, the fusion of a Functional Mock-up Unit (FMU), a numerical ODE solver and an artifical neural network, we are paving the way for the use of a variety of white-box models from different modeling tools as parts of hybrid models. This contribution handles the hybrid modeling of a complex, real-world example: Starting with a simplified 1D-fluid model of the human cardiovascular system (arterial side), the aim is to learn neglected physical effects like arterial elasticity from data. We will show that the hybrid modeling process is more comfortable, needs less system knowledge and is therefore less error-prone compared to modeling solely based on first principle. Further, the resulting hybrid model has improved in computation performance, compared to a pure first principle white-box model, while still fulfilling the requirements regarding accuracy of the considered hemodynamic quantities. The presented techniques are explained in a general manner and the considered use-case can serve as example for other modeling and simulation applications in and beyond the medical domain.

#### Two-time nonlinear Fokker-Planck equations: A tool for determining the autocorrelation structure of responses to systems under colored noise

Ilias Mavromatis1 , Konstantinos Mamis2

1Columbia University, Civil Engineering and Engineering Mechanics, United States
2Hellenic Naval Academy, Mathematical Modeling and Applications Laboratory, Greece

###### Abstract

In this work, we derive an evolution equation for the joint probability density function of the response in two time instances, for a scalar system subjected to colored, i.e. correlated, Gaussian noise excitation. Similarly to our previous relevant works, a non-local closure is needed for such a derivation, due to the correlated nature of the random excitation. This leads to an evolution equation that is identified as nonlinear Fokker-Planck equation. As preliminary assessment of this new two-time nonlinear Fokker-Planck equation, we examine: i) its validity in the case of a linear system, in which it yields the correct Gaussian distribution as its unique solution, ii) its compatibility with the highly-accurate one-time nonlinear Fokker-Planck equations we have recently derived, iii) a first estimation of the stationary two-time autocorrelation function, derived from the said equation, for the case of a bistable system excited by Ornstein-Uhlenbeck noise.

#### Influence of spatial - temporary non-locality effects on the spread of coronavirus infection

Igor Kudinov1

1Samara State Technical University, Department "Theoretical Foundations of Heat Engineering and Hydromechanics", Russian Federation

###### Abstract

Since December 2019, a new coronavirus infection, currently claiming the lives of more than 4,000,000 people, has appeared in the world. Scientists from many countries are developing vaccines, medicines and other means of protection against the COVID-19 epidemic and new coronavirus infections. To understand the way to resist the rapid spread of coronavirus infection, it is necessary to develop a mathematical model of the spatial – temporary virus spread as close as possible to real conditions. In this article, a new locally nonequilibrium mathematical model of the coronavirus infection spread is developed. This model differs from the known ones in taking into account several parameters that are important for the most accurate description of the infection spread, namely: relaxation time, characterizing the infection inertia; relaxation coefficient, taking into account the change rate in the dynamics of infected and susceptible people, and the spatial nonlocality coefficient, taking into account the infection spread over long distances from closed zones (by air, rail, road, etc. types of movements).

#### Soliton solutions of the cubic-quintic complex Ginzburg-Landau equation in the presence of higher-order effects

Mário Ferreira1

1University of Aveiro, Department of Physics, Portugal

###### Abstract

The soliton perturbation theory is used to obtain the steady-state solutions of the cubic-quintic complex Ginzburg-Landau equation (CQCGLE) in the presence of higher order effects, namely, the intra-pulse Raman scattering (IRS) and the third order dispersion (TOD). Linear stability analysis is employed to study the steady-state solutions and the results are verified by numerically solving the propagation equation. Very high-amplitude solitons are found near a singularity which occurs when the nonlinear gain saturation vanishes. This singularity is no longer present in the presence of the IRS effect. The predictions from perturbation theory are confirmed by numerically solving the CQCGLE.

#### Finding chaos in cardiac electrophysiology

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

###### Abstract

Our life depends on the regular beating of the human heart. Without this movement, there is no distribution of oxygenated blood in the human body, and vital tissues are damaged within minutes. The heart's activity is controlled by electrical signals gradually propagated through the cardiac tissue from one cell to another. This paper deals with studying the dynamic properties of this electrophysiological system and looks for cases during which this communication between cells is disrupted. For these purposes, a mathematical model of cardiac electrophysiology is used, thanks to which it is possible to study this propagation in various conditions without endangering human life. The responses of cardiac cells to different amplitudes and frequencies of stimulation are then analyzed using modern methods of examining dynamic systems such as the 0-1 test for chaos, Recurrence quantification analysis, entropy calculation, etc., which detects dangerous conditions during which the heart cannot function properly.

###### 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 approach to the implementation of a recommendation platform for proton therapy centers

Eugenia Echkina1 , Anton Budnyak2 , Natalia Guzminova3

1Moscow State University , Department of Computational Mathematics and Cybernetics, Russian Federation
2Lomonosov Moscow State University, The faculty of Computational Mathematics and Cybernetics, Russian Federation
3Springwood Capital Ltd (UK), , United Kingdom

#### Including group velocity dispersion into a full-wave numerical solver for the Maxwell-Liouville-von Neumann equations

Lukas Seitner1 , Johannes Popp2 , Michael Riesch3 , Michael Haider4 , Christian Jirauschek5

1Technical University of Munich, Department of Electrical and Computer Engineering, Germany
2Technical University of Munich, Department of Electrical and Computer Engineering, Germany
3Technical University of Munich, Department of Electrical and Computer Engineering, Germany
4Technical University of Munich, Department of Electrical and Computer Engineering, Germany
5Technical University of Munich, Department of Electrical and Computer Engineering, Germany

###### Abstract

As many molecules have their rotovibrational resonance frequencies in the mid-infrared or terahertz regime, efficient generation of corresponding frequency combs may lead to large progress in gas spectroscopy and sensing. Quantum cascade laser's (QCLs) are among the most promising candidates for a compact and cheap radiation source in this frequency range. This contribution presents a full-wave numerical solution of the Maxwell-Liouville-von Neumann equations, thus avoiding the limited applicability of the rotating wave approximation to moderate field strengths and spectral bandwidths only. We include losses and chromatic dispersion of the optically active material in the QCL. The semi-classical approach uses the finite-difference time-domain (FDTD) method to derive update equations for the electric field, starting from the one-dimensional Maxwell equations. There, the electronic quantum system is coupled to the optical full-wave propagation via a polarization term that arises from the evolution of the density matrix. Furthermore, dispersion effects are considered through a classical polarization term and losses are introduced by a finite material conductivity. This work mainly focuses on the integration of group velocity dispersion (GVD) into the update equations. It is known to be one of the main degradation mechanisms of terahertz frequency combs, but has not yet been added to the existing full-wave solver. The implementation is carried out as Lorentz model and is applied to an experimentally investigated QCL frequency comb setup from the literature. The reported results are in good agreement with the experimental data. Especially, they confirm the need for dispersion compensation for the generation of terahertz frequency combs in QCLs.

#### Advanced selection of ensemble control tools

Alex Samoletov 1

1University of Liverpool, Department of Mathematical Sciences, United Kingdom

###### Abstract

Molecular dynamics (MD) is an inevitable companion of research in a range of disciplines in natural sciences including such branches as the design of new functional materials and the drug discovery. MD simulation (like laboratory experiments) is performed under certain environmental conditions, usually at fixed temperature and pressure. The concept of thermodynamic temperature is essentially phenomenological, but an MD dynamic temperature control tool must measure temperature as an average over time. Thus, we need a function of dynamic variables such that the temperature can be expressed by averaging of this function over time along the trajectory in the phase space of the system, under the assumption of ergodicity. However, there is no unique function of dynamic variables corresponding to thermodynamic temperature, and the expression for temperature can take alternative forms. In this regard, it is not surprising that various dynamic temperature control schemes have been proposed and implemented in equations of motion in the form of mathematical tools, called the thermostat. In this presentation, we will take a quick look at our concept of dynamic ensemble control, which naturally leads to the concept of temperature expression, formulated in precise mathematical form. We then propose a mathematical scheme for generating a wide range of temperature expressions and relate it to the theory of special functions. We find a connection between the temperature expressions and the Appell sequences. Joint work with B. Vasiev (University of Liverpool)

###### Acknowledgements:

This work has been supported by the EPSRC grant EP/N014499/1

#### Adaptive Wavelet Packets in Spatial Domain for Rayleigh Backscatter Spectrum Estimation in Optical Frequency Domain Reflectometry

Nandini Basumallick1 , Dipten Kumar2 , Somnath Bandyopadhyay3

1CSIR-Central Glass and Ceramic Research Institute, Fiber Optics and Photonics Division, India
2CSIR-Central Glass and Ceramic Research Institute, Fiber Optics and Photonics Division, India
3CSIR-Central Glass and Ceramic Research Institute, Fiber Optics and Photonics Division, India

###### Abstract

Optical Frequency Domain Reflectometry (OFDR) is a popular distributed fiber optic sensing technology for measuring physical parameters like strain, temperature and vibration of a structure. In this method, the frequency of the source laser is continuously swept and the beating interference between the source light and the backscattered light from the fiber under test (FUT) is captured by a photodetector (PD). A Fourier Transform (FT) of the signal captured by the PD gives the backscattered intensity as a function of location on the fiber. The Rayleigh backscattered light from each location changes as the local Rayleigh backscattered spectrum (RBS) shifts with variation in local strain or temperature. In order to quantify the RBS shifts, conventionally a Short Time Fourier Transform (STFT) is applied. In this method a sliding window of fixed number of points is taken at each location and the FT of this window gives the RBS at that location. A disadvantage of this method is that there is a trade off between the spatial and spectrum resolution. In this paper, we propose an OFDR signal demodulation method using Adaptive Wavelet Packets (AWP), which facilitates a signal specific selection of a variable window length and position along the FUT depending on entropy based best basis selection. The AWP is applied in spatial (beat frequency) domain, which is simpler than applying AWP in time domain as it does not require generation of a wavelet function, decimation/ interpolation or antialiasing/image rejection filters. This method is advantageous as it provides finer spatial resolution at locations of interest, where usually weak Fiber Bragg Gratings (FBGs) are inscribed, compared to other locations on the fiber, thus saving the computational load. Also, the spatial resolution adapts to the length of the FBG, thus providing the best RBS shift resolution for that location. The spatial resolution is not allowed to be lower than a certain cut off, so as to maintain the desired RBS shift resolution. The method is evaluated using simulations for fibers with gratings at different locations, lengths and spacing and could detect a RBS shift as low as 10 pm with 2.5 mm spatial resolution. The method could estimate RBS shift upto 2 nm with 10 pm resolution, for a dense FBG array subject to a strain chirp as experienced by a fiber mounted on a cantilever.

#### Estimating the strength and stiffness of damaged beam-column joints using geometric integration in image processing methods.

1Shahid Beheshti University, Civil Engineering, Iran (Islamic Republic of)
2Shahid Beheshti University , Faculty of Civil, Water and Environmental Engineering, Iran, Islamic Republic Of
3Shahid Beheshti University, , Iran, Islamic Republic Of

###### Abstract

An extensive database of 1000+ surface cracks images from cyclic test results of 200+ specimens at various drift ratio levels are collected. The database covers a broad range of concrete compressive strength, rebar and stirrup strength, beam length to depth ratio, joint aspect ratio, etc. Empirical equations are presented that updated stiffness and strength of beam-column moment frames according to the corresponding crack pattern. The equations are based on geometric integrations in image processing methods. Three scenarios are considered based on the availability of the input data and for each scenario a unique equation is presented. It is shown that the accuracy of the perdition is enhanced as more characteristic information is available. Interestingly, solely having the crack pattern as the input data provides a high level of accuracy for the damage state evaluation.

#### A benchmark study on the model-based estimation of the go-kart sideslip angle

Vincenzo Maria Arricale1 , Michele D'Inverno2 , Alessandro Zanardi3 , Emilio Frazzoli4 , Aleksandr Sakhnevych5 , Francesco Timpone6

1University of Naples "Federico II", Department of Industrial Engineering, Italy
2University of Naples "Federico II", , Italy
3ETH Zürich, , Italy
4ETH Zürich, , Italy
5University of Naples "Federico II", , Italy
6University of Naples "Federico II", , Italy

###### Abstract

Nowadays, the active safety systems that control the dynamics of passenger cars usually rely on real-time monitoring of vehicle side-slip angle (VSA). The VSA can't be measured directly on the production vehicles since it requires the employment of high-end and expensive instrumentation. To realiably overcome the VSA estimation problem, different model-based techniques can be adopted. The aim of this work is to compare the performance of different model-based state estimators, evaluating both the estimation accuracy and the computational cost, required by each algorithm. To this purpose Extended Kalman Filters, Unscented Kalman Filters and Particle Filters have been implemented for the vehicle system under analysis. The physical representation of the process is represented by a single-track vehicle model adopting a simplified Pacejka tyre model. The results numerical results are then compared to the experimental data acquired within a specifically designed testing campaign, able to explore the entire vehicle dynamic range. To this aim an electric go-kart has been employed as a vehicle, equipped with steering wheel encoder, wheels angular speed encoder and IMU, while an S-motion has been adopted for the measurement of the experimental VSA quantity.

#### Modelling a mechanical antenna for a calibrator for interferometric gravitational wave detector using finite elements method

Carlos Frajuca1

1FURG, IMEF, Brazil

###### Abstract

Interferometric gravitational wave detectors (IGWD) are a very complex detector, the need to lock the detector in a dark fringe condition besides the vibrations that affect the mirrors, creates the necessity of using active suspension systems. These active system make the system to 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 detector are easily calibrated. This work aims to design the mechanical antenna of such calibrator. The main difficult is to design the calibrator is the frequencies required to make the detection. These massive detectors usually were made in frequencies close to 1 kHz and the frequency range to operate for better sensitivity is around 100 Hz. The antenna is modelled in finite elements method and a design of such antenna is presented.

###### Acknowledgements:

Carlos Frajuca acknowledge FAPESP for grants #2013/26258-4 and #2006/56041-3.

#### Obtaining the sensitivity of a calibrator for interferometric gravitational wave

Carlos Frajuca1

1FURG, IMEF, Brazil

###### Abstract

Interferometric gravitational wave detectors (IGWD) are a very complex detector, the need to lock the detector in a dark fringe condition besides the vibrations that affect the mirrors, creates the necessity of using active suspension systems. These active system make the system to 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 detector are easily calibrated. This work aims to obtaining the expected sensitivity of such calibrator by using lumped modelling in such mechanical detector. The calibrator is modelled as spring mass system and the sensitivity curve is presented calculated in by a matlab program. The curve shows that using state of art parameters for the detector the final sensitivity is close to que quantum limit and can be used to calibrate the IGWDs.

###### Acknowledgements:

Carlos Frajuca acknowledge FAPESP for grants #2013/26258-4 and #2006/56041-3.

#### Monitoring the brightness temperature of the Moon throughout the lunar cycle from radio observations in the Ku band

David Galeano1 , Edwin A. Quintero2

1Universidad Tecnológica de Pereira, Astronomical Observatory, Colombia
2Universidad Tecnológica de Pereira, Astronomical Observatory, Colombia

###### Acknowledgements:

The authors express their gratitude to the Vicerrectoría de Investigaciones, Innovación y Extensión of the Technological University of Pereira, Colombia, for its financial support in the execution of the research project “Evaluación de las Capacidades Científicas y Didácticas del Radiotelescopio en Banda KU del Observatorio Astronómico UTP”, code 3-21-1.

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

Carlos Frajuca1

1FURG, IMEF, Brazil

###### Abstract

An experiment to measure the speed of gravitational signals in short distances is been developed with the intention to study its behavior when a medium different from air is allocated between the emitter and the detection and check if the speed of the interaction changes. The experiment is composed of three sapphire bars that vibrates, and as they vibrate its creates a tidal gravitational wave signal that interacts with another sapphire bar, this bar is monitored by a very pure microwave signal and its amplitude and phase are measured and the gravity speed is calculated, all system is cooled to a temperature of 4.2 K to increase sensitivity and kept in high vacuum. The sapphire bar need to be suspended to avoid seismic noise and other interferences. This work models the sapphire bar with the suspension, a wire that suspends the bar by its center and has its performance calculated in a finite element modelling. The final result shows that the mechanical behavior of the sapphire bar is not affected by the suspension.

###### Acknowledgements:

Carlos Frajuca acknowledge FAPESP for grants #2013/26258-4 and #2006/56041-3.

#### Obtaining the frequencies of Schenberg detector sphere using finite element modelling

Carlos Frajuca1

1FURG, IMEF, Brazil

###### Abstract

The resonant-mass gravitational wave detector SCHENBERG is a spherical detector that operates with a central frequency close to 3200 Hz and a bandwidth of around 200 Hz. It has a spherical mass that work as an antenna which weight is 1150 kg and is connected to the outer environment by a suspension system designed to attenuate local noise due to seism as well as other sources, 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 should be monitored by six parametric microwave transducers whose output signals will be 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 for mount the transducers and the central hole for where 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 it is compared to the experimental results.

###### Acknowledgements:

Carlos Frajuca acknowledge FAPESP for grants #2013/26258-4 and #2006/56041-3.

#### Analytical modelling of a novel test for determination of porosity and permeability of porous materials

ROBERTO TORRENT1 , Guillermo Zino2

1Materials Advanced Services, Technical Services, Switzerland
2Materials Advanced Services Ltd., , Argentina

###### Abstract

Porosity and permeability are important properties of porous materials, such as rocks and concrete. This paper presents the physical-mathematical modelling of a novel test, based on one previously developed by one of the authors (standardized in Switzerland, Japan and China) for measuring the air-permeability of concrete structures. In the present case, a cylindrical laboratory specimen is placed in a tight cell, subjected to an initial vacuum pressure P0, which is afterwards isolated. The rate of pressure increase (due to the extraction of air originally at atmospheric pressure Pa) is related to the coefficient of permeability of the material whilst the final pressure attained is a function of the porosity (total amount of air extracted). The analysis assumes a unidirectional radial flow of air, which can be achieved by a special three-chamber vacuum cell (with pressure regulation of the external chambers) or by an air-tight sealing of the extreme faces of the cylinder. The analysis is developed under the assumption of viscous laminar flow. To account for the molecular diffusion flow, the test can be performed under vacuum (P0 &lt; Pa) and under overpressure (P0 &gt; Pa), enabling the application of the Klinkenberg correction to get the intrinsic coefficient of permeability.