Table of contents

The Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences organized its 15th annual conference of the series AMiTaNS (Application of Mathematics in Technical and Natural Sciences). The event took place during June 21-26, 2023 in the Congress Centre of Black-Sea resort of Albena, Bulgaria. Its aim was to foster existing and new personal contacts, scientific discussion as well as to provide a forum for the exchange of ideas and experience between specialists in the fields of Mathematics, Physics, Biology, Ecology, Economics, Computer Science and Technology. The event became a world conference covering 15 time zones between Chile and Nebraska through Texas, Indiana, Alabama, Florida, the UK, Europe, Cyprus, Russia, and China. The conference was managed from the Congress Centre in Albena where 40 participants and delegates were present in person and the other 40 attended the event via Zoom video platform.

Interest in this conference is growing year by year. This year we registered 70 talks and scientific reports, more than 80 participants – contributors and delegates from 16 countries around the world, representing the continents of Europe, North and South America, and Asia. About 18% of them attended the conference for the first time, with 50% of them being young scientists. The accepted talks were delivered and attended both on-location at the big hall and Corolla hall in Flamingo Grand hotel and on-line. Every day the morning sessions started by plenary lectures followed by contributed sessions on the following topics: Applied Analysis, Biomathematics, Continuum Mechanics, Mathematical Physics, Numerical Methods, Scientific Computing. As part of the program, leaders of their respective fields organized three special sessions: Statistics & Modeling, Mathematical Methods in Reliability Theory, Algebraic and Geometric Aspects of Integrable Systems. A number of very interesting presentations were delivered, which sparked stimulating scientific discussions both on- and off-line. The reader can find comprehensive and detailed information about the talks and reports including their records on the conference website at http://2023.eac4amitans.eu.

All contributed manuscripts were reviewed by anonymous independent referees via Morressier platform, and the approved revised manuscripts were accepted for publication in the present volume. The continued success of AMiTaNS in defiance of the extraordinary circumstances and challenges faced in the last few years undoubtedly enhances its reputation as an established annual meeting with an eminent and continuously growing core of contributors. Yet, the hybrid format turned out very flexible both for the organizers and contributors. It makes the conference accessible to all those who wish to attend either in person or remotely. We would like to thank the plenary speakers, who accepted our invitation and contributed to the conference through their elucidating lectures. We would also like to thank the special sessions organizers, hosts and co-hosts for the high scientific quality of the talks they selected, and for ensuring the smooth running of the conference in hybrid format. We are deeply indebted to the scores of anonymous referees all over the world, who approached their duties very professionally and thoroughly, and helped us to maintain high scientific standards. We highly appreciate the involvement of the members of the Program Committee and Steering Committee, who supported AMiTaNS from its inception, and worked tirelessly throughout the intensive labors of advertising, arranging, organizing, and reviewing. Special thanks go to our colleagues from the University of Essex at Colchester, UK, who worked with dedication so that parallel Zoom conference sessions could be held completely on-line.

We are very grateful to our publisher Institute of Physics, Bristol, UK for the helpful cooperation during the preparation of this volume.

List of Program Committee, Organizer, Sponsor, Participants are available in this Pdf.

All papers published in this volume have been reviewed through processes administered by the Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

• Type of peer review: Single Anonymous

• Conference submission management system: Morressier

• Number of submissions received: 86

• Number of submissions sent for review: 53

• Number of submissions accepted: 48

• Acceptance Rate (Submissions Accepted / Submissions Received × 100): 55.8

• Average number of reviews per paper: 1.0416666666666667

• Total number of reviewers involved: 32

• Contact person for queries:

Name: Michail Todorov

Email: mditod@gmail.com

Affiliation: EAC4AMiTaNS - Mathematical Modelling and Numerical Methods

Hypertension (HT) is a major risk factor for heart disease, stroke, and kidney disease. A diagnosis of HT is based on two or more blood pressure (BP) readings taken on two or more visits, and such diagnosis may vary depending on the threshold BP values utilized by specific guidelines. Our hypertension identification approach has been recently proposed and validated for HT diagnosis and could be used as ground truth in modeling of latent HT diagnosis. Our approach to modeling of latent HT diagnosis with high precision will leverage analytics to "Big Data", such as electronic health records (EHRs). In this work, we will review the time complexity underlying the classical ML methods XGBoost (XGB) and Artificial Neural Networks (ANN). In particular, we compare the XGB and ANN to leverage their strengths. The performance of all algorithms for diagnosing HT will be characterized using the area under the curve (AUC) approach on a big EHR longitudinal dataset. Predictor variable importance and model interpretability will be assessed using the Shapley values approach.

High levels of air pollution are dangerous to human health, which is a current problem for densely populated cities worldwide. Studying this problem can help detect pollutants' time dependencies on basic meteorological measurements and other factors for future prediction and elaborate corresponding alarms when official upper pollution limits are exceeded. In this work, time-causal models based on previous daily time observations and meteorological measurements in the city of Plovdiv, Bulgaria, are applied. Vector-type temporal-causal models are constructed and analyzed for carbon dioxide (CO2), nitrogen dioxide (NO2), sulfur dioxide (SO2), and fine dust particles below size 10, 2.5, and 1 micron (PM10, PM2.5, and PM1), respectively. Pollution levels are predicted seven days ahead.

Exceeding the norms and limits of atmospheric air pollution causes enormous damage to the population's health and the environment. Determining the factors affecting air quality is a current task in a local, regional, and global scale. In this study, we use daily time series data for the main air pollutants in Burgas, Bulgaria – O₃, NO, NO₂, CO, SO₂, and PM₁₀, to analyze, model, and forecast these levels depending on meteorological factors. For this purpose, the stochastic ARIMA method and ARIMA with transfer functions are applied. Results are obtained for univariate and multivariate time series. Particular attention is paid to the concentrations of the secondary pollutant ground-level ozone (O₃), which are modelled as a function of all variables considered. Results were evaluated using root mean square error, mean absolute percentage errors, and the coefficient of determination. Short-term forecasts have been obtained for seven days ahead. Model accuracy up to 84% has been established.

A mathematical framework has been formulated to elucidate the conductivity behavior of polymer composites infused with carbon nanoparticles. This linear model, while simplistic, provides a foundational understanding of how factors like nanoparticle morphology, concentration, and surface properties, in conjunction with polymer matrix attributes such as viscosity and surface tension, influence the spatial distribution of these nanoparticles. The overarching aim is to harness the potential of electrically conductive composites in bolstering green technological advancements in sectors like road transport, solar energy, batteries, and environmental conservation. The model underscores the pivotal role of high electrical conductivity in ensuring the efficient, sustainable, and environmentally benign operation of these technologies. This mathematical construct emerges as an instrumental tool, paving the way for the strategic design and optimization of electrically conductive composites tailored for diverse green technology applications.

In the EU there are many regulations for monitoring the air contamination, for different norms of the air pollutants and aims for improving the air quality. Bulgaria as a member of the European Union has to comply with all these regulations.This paper deals with PM air contamination in the city of Vidin, Bulgaria. Vidin is located in northwestern Bulgaria, on the south bank of the river Danube. On the other side of the Danube is the town of Calafat, Romania. In Vidin during the winter periods of the years there are PM, sulfur and carbon dioxides air pollution greater than accepted norms. Due to the lack of central heating, the population uses mainly solid fuels for heating both in the domestic and in the public sectors. In Vidin there are days with PM10 pollution greater than the daily norm of 50μg/m³. This paper aims to study PM10 air pollution in the city of Vidin, Bulgaria for the period 2012 – 2022.

Polluted air has a negative impact on human health and plant and animal life. There are two types of sources of air pollution: human activity (transport, heating, industry and others) and natural phenomena such as natural fires, volcanic activity, deforestation and others. Substances that are the most common air pollutants are dust particles, carbon and nitrogen dioxides, carbon and nitrogen oxides, hydrocarbons; aldehydes; radioactive substances, heavy metals, sulfur dioxide, ozone, etc. Gaseous air pollutants of primary concern in urban environments include sulfur dioxide, nitrogen dioxide, and carbon monoxide. Sulfur dioxide is a colorless gas that is a product of volcanic eruptions and various industrial processes. It's usually released when coal and oil are burned. Nitrogen oxides, especially nitrogen dioxide, are poisonous gases with a pungent, suffocating odor. There are many regulations aimed at air pollution and pollution monitoring for all European countries. Bulgaria, as part of the EU, must comply with all these regulations. There are still many places and periods of time in Bulgaria over the years with air pollution greater than daily norms. The present study is dedicated to the study of air pollution with gaseous substances in the area of Svishtov, Bulgaria. The town of Svishtov is located in Northern Bulgaria, on the banks of the Danube River, where the southernmost point of the river along its entire length is located. A statistical analysis of the level of air pollution in Svishtov based on official data from the monitoring station in the city is presented. The measurements cover the period 2021 - 2023. All research results are presented graphically and commented.

It is crucial to establish a seasonal dependence on the levels of marine biotoxins in the Black Sea to impose seasonal prohibitions on the gathering of marine species in this sea and safeguard human health. Fisher's analysis of variance (ANOVA) is a statistical technique for assessing how various variables affect a collection of data. In some cases, research must be carried out in an uncertain environment, with missing or insufficient data. An approach for solving this imprecision when a data set occurs in an ambiguous context is intuitionistic fuzzy logic, which Atanassov introduced in 1983. Compared to fuzzy data, intuitionistic fuzzy (IF) data also has a hesitation degree. In 2020, we first suggested the one-way (1-D) IFANOVA and the software utility for its performance, combining traditional variational analysis with modeling opportunities of Index Matrices (IMs) and Intuitionistic Fuzzy Sets (IFSs). The current study focuses on 1-D IFANOVA of the distribution of marine biotoxins in the Black Sea by the "season" factor on the IF dataset of the number of marine biotoxins for the period from February 1 to July 31, 2021. We will also compare the findings of 1-D IFANOVA and conventional ANOVA performed on the identical data set.

Researching consumer demand in the market for goods is essential for any business. The purpose of this study is to forecast the demand for furniture from a large manufacturer in Bulgaria. Significant factors influencing customer flow, both in the company and online stores, are investigated. Daily observations for nearly two years are modelled using CART Ensemble with arcing. The constructed models describe the demand for furniture with high goodness-of-fit statistics: coefficient of determination up to 93% and determine the order of the factors influencing the demand.

This paper reports the development of a positron imaging method for in vivo single-cell tracking under high-noise conditions. Following biological processes spatially and temporally at a single-cell level in a living organism is desirable for inquiring into the relationships between the behaviours and properties of cells. Positron-emitting radionuclides enable detecting and following radioactivity-labelled substances deep inside living organisms. However, positron imaging has several challenges, such as the distribution of high noise in other areas close to the cell under investigation. In this work, an algorithm for locating a cell with millisecond resolution to combat the strong interference of nearby noise is developed. The feasibility of the method is verified by the demonstration of particle tracking and detection of behavioural changes in an environment with the signal-to-noise ratio of 1:9.

This paper deals with nonlinear first-order impulsive functional-differential equations of neutral type with variable coefficients. The asymptotic behaviour of the non-oscillating solutions of such equations is investigated as a function of the values of the variable coefficient in the neutral term to serve as a basis for further studies of the oscillation of the solutions of such equations.

In this work, the approximate analytical solutions of the Generalized Hydrodynamic Equations (GHE) for turbulent flow in channel is presented. The general solution is a superposition of the laminar (parabolic) and turbulent (superexponential) solutions. The analytical solution compares well with the experimental data by Van Doorne (2007) and Nikuradse (1933).

It is proposed to explain the nature of turbulence as oscillations between the laminar (parabolic) and turbulent (superexponential) solutions. The suggestion is confirmed by comparing the results for turbulent velocity fluctuations of the analytical formula with the experiment by Van Doorne (2007). The Navier-Stokes equations do not have the superexponential solution.

The obtained analytical solution provides a complete structure of the turbulent boundary layer that compares well with the experiments by Wei and Willmarth (1989).

This work is focused on investigation of radiation effects in Ultra-Thin Silicon solar cells with a particular emphasis on electron irradiation. The study is motivated by the application of these solar cells, developed by Solestial, Inc., for powering space missions, including those led by NASA, the Department Of Defence (DOD), and commercial satellite missions. Our research encompasses both experimental and theoretical approaches, addressing unique challenges posed by ultra-thin solar cell technology that deviates from the traditional models. From the experimental point of view, the test structures were irradiated with 1 MeV electrons up to the fluence of 1E+15 e/cm². Radiation effects due to accumulated electron dose were noticed as a drop in open-circuit voltage (V_oc). An analytical expression for modeling the Voc characteristic of the UT-Si cell after exposure to electron irradiation was formulated and subsequently compared with experimental data. The theoretical foundation of the proposed approach builds upon the Non-Ionising Energy Loss (NIEL) concept, a fundamental parameter in addressing radiation damage modelling and survivability predictions.

The approach to efficiency improvement of space 3-Junction and 2-Junction solar cells, that involves a layer of down-converting material on the top of the cell, is presented. The layer consists of a polymer nanocomposite coating impregnated with the nanoparticles of inorganic compounds (fluorides or oxides) doped with rare earth ions down-converting solar UV light to visible matching the spectrum of the responsivity of the cell. Computational model of a solar cell is presented and used for processing the experimental data. Experimental results demonstrate an increase of the generated current and photoelectric efficiency.

This paper presents a study of noise pollution in the cabin of a passenger car in the context of various types of road. The purpose of the study is to understand how the type of road surface can influence the levels of noise inside the car. Sound pressure levels were measured on the A-scale of a sound level meter for 3 types of road surface - crushed stone pavement, asphalt, and cobblestone. The study was conducted at varying speeds of the car within the range of 10-60 km/h. Due to limitations of homogeneous road conditions, a duration of 10 seconds was chosen for each measurement. The sound level meter was placed at a selected measuring point, close to the driver's head. On the data collected in the above-mentioned way, various regression models have been developed to assess the impact of speed and type of road surface on the noise level. It was found that the noise level increases with the roughness of the road surface, and the resulting risks were analysed.

We have developed a method called the two-dimensional Padé-type approximants method, which can be used to reduce the Gibbs phenomenon in the harmonic two-dimensional Fourier series. This method can be applied to both monochrome and color raster images. To do this, we implement the generalized two-dimensional Padé approximation proposed by Chisholm. In this approach, we select the range of frequency values on the integer grid according to the Vavilov method. We propose a definition of a Padé-type functional and provide examples of its application to simple discontinuous templates represented as raster images. Through this study, we are able to draw conclusions about the practical usage and advantages of the Padé-type approximation. We demonstrate that the Padé-type approximant effectively eliminates distortions associated with the Gibbs phenomenon, and it is visually more appropriate than the Fourier approximant. Additionally, the application of the Padé-type approximation reduces the number of parameters without sacrificing precision.

Sixth-order boundary value problems (BVPs) arise in thin-film flows with a surface that has elastic bending resistance. To solve such problems, we first derive a complete set of odd and even orthonormal eigenfunctions — resembling trigonometric sines and cosines, as well as the so-called "beam" functions. These functions intrinsically satisfy boundary conditions (BCs) of relevance to thin-film flows, since they are the solutions of a self-adjoint sixth-order Sturm–Liouville BVP with the same BCs. Next, we propose a Galerkin spectral approach for sixth-order problems; namely the sought function as well as all its derivatives and terms appearing in the differential equation are expanded into an infinite series with respect to the derived complete orthonormal (CON) set of eigenfunctions. The unknown coefficients in the series expansion are determined by solving the algebraic system derived by taking successive inner products with each member of the CON set of eigenfunctions. The proposed method and its convergence are demonstrated by solving two model sixth-order BVPs.

A hollow viscoelastic right circular cylinder subjected to a time-dependent load is considered. The cylinder is with finite dimensions. A transient load acts upon the inner surface of the cylinder, whereas no loads are applied to outer surfaces. The end surfaces of the cylinder are restrained to move along the cylinder axis. The viscoelastic behaviour of the material is modelled using Boltzmann – Volterra equations. A yield criterion is implemented in the numerical analyses. By assumption, upon reaching the yield surface, the linear viscoelastic model switches to a plastic constitutive relation. The transient dynamic behaviour of the material is simulated for different intensities of the applied load and model parameters.

Advancements in acquiring, storing and processing information have led to a significant accumulation of large databases in the field of metagenomics—a branch of biology that deals with the study of genetic material directly recovered from environmental or clinical samples. The data collected from metagenomic experiments are massive and noisy, often containing fragmented information representing over 10,000 species. Processing and analyzing this data require software installed on supercomputers. In this paper, the authors present the design, development, and creation of a computational server system aimed at processing and analyzing bioinformatics data in metagenomics and 16S rRNA gene studies. They utilized the specialized software product Galaxy Europe for this purpose. The analysis was performed using the metagenomics-based method Targeted Amplicon Sequencing. The data was divided into three test collections in a special fasta file format. These collections were processed using the web-based Galaxy platform and two configuration variants on a high-performance cluster equipped with NVIDIA Tesla V100 32 GB GPU cards. The analysis process was optimized to reduce information processing time, and the parallel performance of the three different system configurations was investigated for the data used.

In this work we study some characteristics of growth functions of the logistic type. The standard logistic function and the 2-logistic growth function are solutions of ordinary differential equations derived from the perspective of reaction network theory. These solutions are compared in terms of their shape. We are interested in the new 2-logistic probability distribution and its characteristics. Using the tools of reaction network theory and numerical methods we derive some properties of this distribution.

We study the age changes of the anthropometric as well as of the mass-inertial characteristics (MIC) of Bulgarian women aged 18-25 versus those aged 30-40. We do that via mathematical modelling of the human body (HB). Nowadays mathematical modelling is one of the modern methods for the determination of the MIC of different segments of the body, as well as of the whole body, and for studying the changes of the inertial characteristics during a specific motion of the considered person. The current work presents a 3D mathematical model (MM) of the HB, that is also generated in a computer environment. Both the model and its computer generation allow for the calculation of the MIC of all segments of the body, as well as for the whole HB in specific body positions. We consider such body postures which are presented in the corresponding classification of astronauts' standard positions of interest for NASA. The obtained results are compared with those reported in the literature by other authors. The proposed models shall be also helpful in problems appearing in medicine (orthopaedics and traumatology), computer simulations, rehabilitation robotics, and sports, as well as in areas such as ergonomics, simulation of human behaviour in space, forensics (body fall, car crash) and more.

The development of fast and reliable methods for predicting the biological activity of the substances in computational biology is of a great importance. This improves the development of some new compounds while keeping costs low. Among many scientists, an attractive target for docking experiments is the Delta-opioid receptor (DOR) and delta-opioid ligands (DOL). Their biological efficacy can be measured by various techniques, which could facilitate the establishment of the relationship between the structure of the compounds and their biological effect. The relationship between the results of the computer experiments and the biological activity of these compounds is modelled by using machine learning regressors. The primary goal of this study is to determine the most appropriate neural network for modelling the relationship between in vitro and in silico results for DOR and delta-opioid ligands.

Christov functions are a complete orthonormal set of functions on L²(-∞,∞) that allow us to expand derivatives, nonlinear products, and nonlocal (integro-differential) terms back into the same basis. These properties are beneficial when solving nonlinear evolution equations using Galerkin spectral methods. In this work, we demonstrate such a "Christov expansion method" for the Benjamin–Ono (BO) equation. In the BO equation, the dispersion term is nonlocal, given by the Hilbert transform of the second spatial derivative of the unknown function. The Hilbert transform of the Christov functions can be computed using complex integration and Cauchy's residue theorem to obtain simple relations. Then, a Galerkin spectral expansion can be used to the solve the BO equation. Time integration is performed using a Crank–Nicolson-type scheme. Importantly, the Christov expansion method yields a banded matrix for the spatial discretization, even though the spatial terms are nonlocal. To demonstrate the approach and its implementation, we perform numerical experiments showing the steady propagation of single and the overtaking interaction of multiple BO solitary waves.

The rarefied viscous gas flow between a stationary inner and an oscillating outer cylinder is studied in this paper. It is a continuation of our previous publications where we study the flow between the infinite length cylinders while here is considered the case of finite length cylinders bounded by two planes with periodic boundary conditions in the cross sections at the ends of the cylinders. So, on the one hand, this changes the flow character creating conditions for periodic self-organization along the axis of symmetry and on the other hand, the current model is reduced to a flow in a limited volume. A continuum model based on Navier-Stokes-Fourier equations for compressible fluid with first order slip boundary conditions on the cylinders wall and statistical model Direct Simulation Monte Carlo (DSMC) method are used to model the flow. The presented numerical results were obtained after reaching sustained oscillations. Considering the model with cylinders of finite length allows to extend its capabilities and obtain a better fit to real conditions.

In this paper we consider the inverse problems of identifying space-dependent coefficients of the mortality rate of the bees and the rate of contamination of the forager bees by pesticides. The model is described by a weakly coupled system of two reaction-diffusion equations for the spatial distribution of uncontaminated and contaminated foraging bees. Final time t = T observations of the density of uncontaminant and contaminant forager bees are used. We propose two approaches for studying the problems. The first one uses the overspecified information to transform the problems into non-linear parabolic equations involving the solution values at the final time. This allows us to prove, using fixed-point arguments, existence of solution to the inverse problems. The second study employs the concept of the quasi-solution to establish existence of solution to the inverse problems as minimizers of least-square cost functionals.

We study inverse problems of reconstructing the time-dependent right-hand side from point observation in a one dimensional parabolic equation on disjoint intervals. These problems are ill-possed, i.e. very slight errors in the additional input may cause relatively significant errors in the output of the left and right internal right-hand side. In this work, we construct computational algorithms, using the loaded equation method. First, we perform a decomposition with respect to the unknown source of the inverse problem solutions. Then the inverse problems are reduced to a loaded parabolic equation problems. The well-posedness of the inverse problems is studied on the base of loaded equation ones. The numerical performance of the approach is realized by finite difference schemes, solved with decomposition algorithms. Computational experiments show the efficiency of the method.

The approach for calculating the propagation time of a signal between GPS satellites will be summarized, based on the proposed new theoretical approach in several previous publications, as well as the perspectives for future development of the theory. Topics include: 1. Basic notions of inter-satellite communications. 2. Shapiro delay formulae in General Relativity Theory - basic formalism and the necessity to extend the formalism by taking into account the satellite motion on a plane elliptic or space-distributed elliptic orbit. 3. Basic facts about the disturbed motion in celestial mechanics and the necessity to incorporate it in the theory of inter-satellite communications, accounting for General Relativity Effects. 4. Propagation time of a signal, emitted by a satellite on a plane and also space-distributed elliptical orbit in terms of zero-order elliptic integrals and respectively of higher order integrals. Proof of the real-valuedness of the propagation time for all cases as one of the criteria for the correctness of the theoretical approach. 5. New analytical algorithms for calculation of zero-order elliptic integrals in the Legendre form. Relation to two representations in the Weierstrass form. 6. The new formalism of intersecting four-dimensional null cones and the resulting physical notions of the (intersecting)) space-time interval (with the property of being positive, negative or equal to zero) and the (intersecting) geodesic distance (being only positive, because is related to the distance, travelled by light or radio signals). Proof of these properties in the general case and in some partial cases. New numerical estimate E_lim > 45.002510943228 [deg], above which the space-time interval is positive and thus inter-satellite communications between satellites on one plane elliptical orbit are possible. The angular distance of 45[ deg] is typical for the disposition of 8 satellites on one orbit in the Russian satellite constellation GLON ASS, so it might be claimed that such a configuration is favourable from the point of view of inter-satellite communications (with account of GRT effects).

Fractional derivatives have found application in modeling various processes in different fields of science. Finite difference schemes are a main approach for numerical solution of models using fractional differential equations. In this paper we investigate the convergence and order of the numerical solution of two-term ordinary fractional differential equation which uses the L1 approximation of the fractional derivative. Inequalities for the weights of L1 approximation are derived and used to prove the convergence of the L1 scheme for the two-term equation. Conditions for the parameter of the two-term equation and error estimates of L1 scheme are obtained. Experimental results for the order and error of the L1 scheme are presented in the paper.

Parametric spectral analysis methods such as the Prony's method can estimate the frequencies and amplitudes of a signal, conforming to their model, with great precision. At the same time, the addition of noise to the signal can lead to a complete model breakdown which leads to erroneous parameter values. This is especially true for the impulse noise. The article explores several possible algorithms which can be applied to the Prony's method in order to refine the results and make them more noise resistant. Such algorithms include signal segmentation methods where the results of each segment processing influence the final estimate as well as the conceptually related method of point skipping. An approach based on the use of non-Euclidean norms as a measure of the linear algebraic equation system's solution quality is developed and tested. Initially, the methods are applied to model digital signals, comprised of harmonic components with varying complex frequencies and amplitudes. Additive white Gaussian and impulse noise is added to the model signals. The results are then applied to the noisy results of a real-life synthetic aperture synthesis experiment obtained in the intermediate zone of radiation.

This paper reports a detailed study of the flow in cyclone separators, with the use of most up to date computational fluid dynamics simulations, which are validated with positron emission particle tracking (PEPT) experiments tracing the movement of particles through the cyclone. The parameters varied were the viscosity of the carrier liquid, the flowrate and, in the numerical simulations, the inlet configurations of the cyclone, namely one and two inlets and, with the two inlets, a) both at right angles to the cyclone axis and b) angled downwards. The study reveals features of the flow, which have not been seen till now, but are necessary for the understanding and modelling of the separation and purification efficiency of cyclones. The results of the simulations and the close agreement with experiment are a testament to the reliability and accuracy of large eddy simulation (LES), even for flow features as difficult to simulate as the confined strongly swirling flows in cyclone separators. The results show that a contiguous, smooth surface of zero axial velocity does exist and has approximately the shape that has been assumed by modellers. The significant effects of fluid viscosity, underflow and modifications to the inlet are also shown.

The paper investigates the dynamic behavior of a hollow elastic cylinder of finite length, placed in a rigid cylindrical shell, under a sharp change in internal pressure. A numerical solution of a two-dimensional dynamic problem is obtained using the method of spatial characteristics. The stress-strain state of an elastic cylinder is described by a system of hyperbolic equations with two circular conical surfaces as characteristic surfaces. The outer cones correspond to longitudinal waves; the inner ones correspond to transverse waves. The calculations were carried out under various conditions at the ends and the outer (contact) surface of the cylinder and shell. An analysis of the results for a cylinder with load-free ends shows that the absence of gluing the outer surface of the cylinder with the shell leads to a significant increase in the velocities of the points of the cylinder. Under the action of internal pressure, the ends move apart, resulting in a significant increase in the radial velocities of the internal channel. Qualitative patterns of behavior of the structures under consideration, which are widely used in mechanical engineering, on impact-type impacts, can be used to improve and optimize them at the design stage.

The numerical solution of partial differential equations is often performed on a numerical grid, where the grid points are used for estimating the partial derivatives. The grid can be fully static as in Eulerian type of solution method, or the grid points can move during the solution, which is the case in Lagrangian type of method. In the current article, a numerical solution method is presented, where the grid points are located on iso-contours of the two-dimensional field. The method calculates the local movement of the iso-contours according to an evolution equation described by the PDE, and the solution proceeds by moving the grid points towards the calculated direction. Additional stability is obtained by setting the grid points to move along the iso-contour line. To exemplify the application of the method, numerical examples are calculated for the two-dimensional diffusion equation.

Opiates are among the oldest drugs that are used to treat many medical problems. They are analgesic and sedative drugs that contain opium. The morphine is its most active ingredient and it is a widely used pain reliever despite its side effects. The main objective of this study is to construct a model which gives the structure-activity relationship among a series of mu-opioid ligands and molecular docking results. For this purpose, a model of mu-opioid receptors using machine learning is introduced. By obtaining a relationship between the docking results and the in vivo test, we could predict the biological effect of the newly synthesized ligands.

Friction plays a crucial role in the formation of contact problems, particularly through adhesion. This paper focuses on a quasi-static three-dimensional problem of a punch movement along the boundary of an elastic half-space. The investigation considers friction and adhesion forces, employing a two-term friction law. The objective is to optimize the pressure distribution beneath the punch. The shape of the punch serves as the design variable, while the deviation of the pressure distribution, originating from a given one, is minimized. The optimization problem can be divided into two sequentially solvable sub-problems. The first task involves finding a pressure distribution that minimizes the performance functional, which has a known solution. The second problem entails searching for the optimal shape of the punch to achieve the previously determined pressure distribution. A numeric-analytical solution is developed based on the expansion of the simple layer potential. The coefficients characterizing friction and adhesion act as small parameters. The proposed method gives the ability to obtain closed-form formulas in each approximation, enabling convenient qualitative analysis and practical engineering applications. The calculations and analytical dependence reveal an asymmetric distribution of pressure on the contact area, during the movement of an axisymmetric punch.

Anomalous diffusion is a non-local process that describes a wide spectrum of natural processes and phenomena with many applications in science and technology. It is described mathematically by the fractional Laplace operator. In this work we examine the integral definition of the fractional Laplacian modeled with the Riesz potential and discretized with the finite element method. The thus obtained system of linear algebraic equations is dense due to the non-local nature of the fractional Laplacian and is computationally complex to solve. With LU factorization, for example, solving the problem has an O(N³) computational complexity, where N is the number of unknowns. However, it can be observed that a large amount of the off-diagonal coefficients have very small absolute values compared to the diagonal coefficients. Those small off-diagonal coefficients can be lumped (set to zero and added to the diagonal coefficient) without significant loss of accuracy. In this work we employ a direct sparse parallel solver to the resultant sparse matrix. We analyze the parallel performance and speed-up, as well as the accuracy, varying the fractional power and the lumping threshold.

Integral equations are of high applicability in different areas of applied mathematics, physics, engineering, geophysics, electricity and magnetism, kinetic theory of gases, quantum mechanics, mathematical economics, and queuing theory. That is why it is reasonable to develop and study efficient and reliable approaches to solve integral equations. For multidimensional problems the existing biased stochastic algorithms based on evaluation of finite number of integrals will suer more from the effect of high dimensionality, because they are based on quadrature points. So we need advanced unbiased algorithms for solving the multidimensional problem which is developed in this paper. A new unbiased stochastic method for solving multidimensional Fredholm integral equations of second kind is proposed and analysed. We compared the newly proposed unbiased algorithm with the old unbiased stochastic algorithm for the one dimensional problem and multidimensional problem.

In this paper we develop advanced multidimensional sensitivity analysis, based on some innovative stochastic approaches for performing air pollution modelling on a large-scale model of long-range transport of air pollutants. The Unified Danish Eulerian Model (UNI-DEM) is a very important mathematical model, and can be applied in many different studies related to damaging effects caused by high air pollution levels. We shall use it in this paper to get a reliable answer to a some very important questions regrading environmental protection. We develop some advanced Monte Carlo and quasi-Monte Carlo methods, based on special lattice and digital sequences. In this paper we will improve the digital ecosystem modeling by improving the existence stochastic approaches. The computational efficiency (in terms of relative error and computational time) of the advanced Monte Carlo algorithms for multidimensional numerical integration has been studied to analyze the sensitivity of UNI-DEM model output to variation of input emissions of the anthropogenic pollutants and of rates of several chemical reactions. The algorithms will be applied to compute global Sobol sensitivity measures corresponding to the influence of several input parameters on the concentrations of important air pollutants. The study will be done for the areas of several European cities with different geographical locations.

A novel version of Monte Carlo algorithm for solving systems of linear algebraic equations is presented and studied. The algorithm is similar to the "Walk on Equations" Monte Carlo method recently developed by Ivan Dimov, Sylvain Maire and Jean Michel Sellier. It is done a comparison with the Gauss-Seidel method for matrices up to size of 2¹². The algorithm could be drastically improved by choosing appropriate values for the relaxation parameters, which in turn leads to dramatic reduction in time and lower relative errors for a given number of iterations. What is more, a sequential Monte Carlo method of John Halton based on an iterative use of the control variate method has been applied. Some of the most important numerical applications are the large system, coming from a finite element approximation of problems, describing a beam structure in constructive mechanics, and the block-diagonal matrices, which come from discretization of models in a regime-switching economy.