Interaction Problems Research Articles

The Monte Carlo Model and Its Application

This research mainly investigated the Monte Carlo model through literature review and case analysis. This research provides an example of the area of a circle to quickly understand what a Monte Carlo model is. Through Monte Carlo, this paper introduced some other algorithms based on it, such as Markov chain, Monte Carlo Markov chain algorithm and Metropolis algorithm. In addition, the Ising model was introduced and it was found that the model can calculate the energy change corresponding to different probabilities of spin acceptance or rejection flip using the Boltzmann distribution at the same temperature. The main objective of this research is that most Ising models occur in high-dimensional states, changing the spin will affect the adjacent spins, and the difficulty of calculating the energy changes increases dramatically with increasing dimensions. Research has found that Monte Carlo methods enable Ising model problems in high-dimensional or complex interactions to be effectively solved through Monte Carlo simulations. Through extensive random sampling and statistical processing, Monte Carlo simulations can estimate the transition behavior of each spin

Review: Animal-assisted intervention for children with attention-deficit/hyperactivity disorder - a systematic review and meta-analysis.

Animal-assisted interventions (AAIs) have emerged as a promising nonpharmacological intervention option for children diagnosed with attention-deficit/hyperactivity disorder (ADHD). However, recent systematic reviews have been primarily narrative. Additionally, the pooled effectiveness of AAIs was absent from these systematic reviews. We conducted a comprehensive systematic review and meta-analysis, searching multiple databases, including Web of Science, MEDLINE, CINAHL, Scopus, PsycINFO, EMBASE and Cochrane, from inception of the databases to March 2024. We retrieved 17 randomised controlled trials or quasi-experimental studies and used Review Manager 5.4.1 software to perform a meta-analysis of the effects of AAIs in treating children with ADHD. We conducted a set of random-effects meta-analyses to estimate standardised mean differences (SMD) with 95% confidence intervals (CI) using subgroup data by different outcome domains extracted from eight randomised controlled trials, in relation to changes in behavioural, mental and physical functioning in a total of 307 children with ADHD before and after the intervention. In comparison with non-AAI groups, AAIs significantly improved attention problems in children with ADHD (SMD = -0.42, 95% CI = -0.71 to -0.13), self-esteem (0.46, 0.14 to 0.78), learning and cognition problems (-0.69, -0.98 to -0.39) and motor proficiency (0.77, 0.11 to 1.42). The pooled effect of AAIs on the severity of ADHD symptoms in the experimental group was not significantly different from the effect of conventional treatments in the control group (0.10, -0.31 to 0.52). Similarly, AAIs had no significant positive effects on social interaction (-0.22, -0.51 to 0.06), social skills (-0.32, -0.87 to 0.24), problematic behaviours (-0.10, -0.54 to 0.35) or emotional problems, including depression and anxiety (-0.13, -0.51 to 0.24). As an ADHD management strategy complementary to gold-standard approaches, such as medication or multimodal interventions, AAIs did not appear to be more effective in improving the majority of core ADHD outcomes in children. Future studies should incorporate rigorous study designs with large sample sizes and a standard protocol to achieve more valid and reliable conclusion.

Neural-network-supported basis optimizer for the configuration interaction problem in quantum many-body clusters: Feasibility study and numerical proof

Neural-network-supported basis optimizer for the configuration interaction problem in quantum many-body clusters: Feasibility study and numerical proof

Influence of energetic heavy ion sputtering on lifetime of alloy target

When energetic heavy ions are incident on negatively charged structure that collects and deposits ions, ion sputtering will occur. Metal wire is a structure commonly used for accelerating ions, the incidence of continuous high-throughput ions can cause surface loss of metal wire, affecting the service performance and lifespan of the metal wire. The SRIM software commonly used for calculating sputtering yield cannot consider the multi-body interaction problem contained in the alloy crystal structure. so, there is a significant error in calculating the sputtering yield of high-energy ions incident on alloy target. Based on the molecular dynamics method and Langevin temperature control model, the calculation model of ion sputtering parameters of energetic metal ions incident on alloy target is established in this work. The model is used to calculate the sputtering yield under the conditions of intact surface lattice of the target material and long-term incident surface lattice damage. The damages to the cathode metal wire under different incident ion fluences are further calculated, and the cross-sectional characterization of the metal wire is carried under typical working condition. The results show that the discrepancy between the experimental value and the theoretical value is less than 10%, which verifies the accuracy and applicability of the theoretical model. Based on this model, the search direction for sputtering resistant materials is proposed, meanwhile, a theoretical optimization is carried out to improve the service life of metal wire, and a method of using Ni-Ti alloy to improve the service life of metal wires is proposed, which is of great significance for predicting the service life of the metal wire under different conditions.

ПСИХОЛОГІЧНА ДОПОМОГА ВІЙСЬКОВОСЛУЖБОВЦЯМ ІЗ ПОСТТРАВМАТИЧНИМ СТЕСОВИМ РОЗЛАДОМ

The article is devoted to the problem of psychological assistance to military personnel who have experienced prolonged combat stress, have acquired traumatic experience and have post-traumatic stress disorder. This condition is interpreted as a mental disorder arising as a result of the military personnel’s experience of psychotraumatic events caused by combat operations. It is manifested throught pathological memories, obsessive return to what was experienced in the war, sleep disturbance, excessive emotional excitability, inadequate readiness to resist, hypersensitivity in the situation of expectation of new extreme conditions. The results of an empirical study are presented, according to which post-traumatic stress disorders were observed in military personnel who were in the combat zone. The negative dynamics of the development of the emotional and cognitive sphere are noted, which is reflected in behavior and a tendency to deviations and aggression. The problem of providing comprehensive professional assistance is actualized, with psychological assistance occuping a prominent role. According to the authors' vision, it should be focused on correcting the social and psychological competence of military personnel, solving their personal problems and problems of interaction with the surrounding world and people around them. Educational, holistic, social and therapeutic directions of psychological assistance to persons with post-traumatic stress disorder are considered. Attention is focused on the psychological and axiological approach as a methodological basis for developing a system of work with military personnel with long-term consequences of post-traumatic stress disorder. Their value-semantic perception of reality opens up possibilities for self-acceptance, acceptance of other people, and establishing interactions with the surrounding world, with themselves and people around them. Prospects for studying the conditions for the deployment of personal and semantic activity of military personnel, their productivity in various types of activity are outlined

Increasing the Environmental Efficiency of the Fleet of Boiler Plants in Modern Conditions

Mankind has created a multi-industry production. Its facilities have a harmful effect on the environment. And it resulted in a global environmental problem that has currently arisen. Among the branches of world production, energy is the most environmentally aggressive, and among its facilities the most aggressive are boiler plants. The purpose of this research is to study the effect of energy facilities on the state of natural environment and analyze the methods to reduce its intensity. Boiler plants are the most important element in modern power engineering. Hence, there is a need for a joint solution of the problem of reducing the harmful effect of boiler plants on the environment and the problem of their useful effect on global energy. The purpose of this research is to analyze methods to solve the problem of environmental interaction of boiler plants with the natural environment in modern conditions resorting to their partial renewal and using alternative energy sources in the future. It is necessary to broaden the requirements to the development of the world fleet of boiler plants that should be based on the use of innovative design, technological and operational solutions to provide reliable environmental efficiency of the equipment. Since domestic boiler plants have worked out a significant part of their service life and create greenhouse gas emissions and pollutant emissions into the atmosphere polluting thus water runoff and producing solid waste, it is advisable to continue to operate them in the mode of partial renewal. The partial renewal results in the reduction of the harmful effect of boiler plants on the environment due to the ecological improvement of the combustion process. Low-power worn-out boiler plants should be stopped and electricity should be supplied to consumers instead of steam. The problem of replacing obsolete boiler plants should be solved by using new energy sources of equivalent power, by creating and commissioning new highly efficient power plants that convert the energy of water, wind, geothermal sources, and solar energy. Understanding the important role of the global fleet of boiler plants in the global environmental situation on the part of international authorities has a positive effect on the state and development of energy and industry. The current involvement of our country in the war has complicated the processes that take place in the energy sector. The quality and reliability of the power plants have acquired particular importance. When using the domestic fleet of boiler plants, it is necessary to do our best to increase its environmental efficiency.

An Echo Pressure Model Based on Mutil‐Gaussian Beam Theory for Measuring the Liquid Level in Special Field

ABSTRACTIn aviation, petroleum and chemical industries and other special areas of production, since the liquid in containers mostly are flammable, explosive, volatile, and corrosive mixtures, the accurate measurement of the liquid level is essential to the real‐time control and production process. In this study, an approximation algorithm based on echo pressure model for measuring the liquid level in special field is proposed in this paper. According to the model, a complete lateral incident ultrasonic measurement system is constructed for the inductive liquid level detection technology in special applications, an algorithm model of the echo pressure is established, which provides the determination of the liquid level relying on the characteristic curve of the echo pressure. The model in this study converts complex interaction problems of sound fields into the echo pressure calculation, which quickly determines performance parameters of sound fields, and a virtual reflection method is used to calculate the sound pressure of the receiving transducer in different states, which reduces computational complexity, finally, through the simulation and experiment, the algorithm is validated. The results are consistent with expectations, and the algorithm can be further applied in practice.

City and factory – the nature of urban planning contradictions

The article deals with the problems of interaction between two functional zones: residential and industrial. It is suggested that there are urban planning contradictions that do not allow the industrial zone to be fully integrated into urban space. Among these, the most significant contradictions are the scale, formation, and planning organization. The study of these contradictions has allowed us to conclude that industrial zones are fundamentally irreducible to residential developments, which leads us to reconsider the placing of industrial zones in cities at the current stage of development.

Fluid-Structure Interaction Analysis of Trapezoidal and Arc-Shaped Membranes Mimicking the Organ of Corti.

In a previous study [H. Shintaku etal., Sensors and Actuators A: Physical 158 (2010): 183-192], an artificially developed auditory sensor device showed a frequency selectivity in the range from 6.6 to 19.8 kHz in air and from 1.4 to 4.9 kHz in liquid. Furthermore, the sensor succeeded in obtaining auditory brain-stem responses in deafened guinea pigs [T. Inaoka etal., Proceedings of the National Academy of Sciences of the United States of America 108 (2011): 18390-18395]. Since then, several research groups have developed piezoelectric auditory devices that have the capability of acoustic/electric conversion. However, the piezoelectric devices are required to be optimally designed with respect to the frequency range in liquids. In the present study, focusing on the trapezoidal shape of the piezoelectric membrane, the vibration characteristics are numerically and experimentally investigated. In the numerical analysis, solving a three-dimensional fluid-structure interaction problem, resonant frequencies of the trapezoidal membrane are evaluated. Herein, Young's modulus of the membrane, which is made of polyvinylidene difluoride and is different from that of bulk, is properly determined to reproduce the experimental results measured in air. Using the modified elastic modulus for the membrane, the vibration modes and resonant frequencies in liquid are in good agreement with experimental results. It is also found that the resonant characteristics of the artificial basilar membrane for guinea pigs are quantitatively reproduced, considering the fluid-structure interaction. The present numerical method predicts experimental results and is available to improve the frequency selectivity of the piezoelectric membranes for artificial cochlear devices.

Implementation of Family Functions in Early Marriage Couples in Padang City

The family has a very important role in preparing quality Indonesian human resources. The function of the family that is carried out can make a significant contribution to the development of its members. Families that can carry out family functions well have the ability to meet the basic needs of family members in facing challenges and making adjustments to changes in themselves and their environment.For family functions to run well, certain conditions must be met such as age, marital status, employment status, level of education, knowledge of family functions, and access to information. This condition is not met for early marriage couples. This research aims to: (1). Identify family functions that can be carried out by couples married at an early age. (2) Analyze the obstacles faced by couples married early in carrying out family functions.This research was conducted in Padang City with a qualitative approach with a descriptive type. Data collection uses in-depth interviews and observations. Informants were determined using snowball sampling. Data was analyzed qualitatively and interpretatively. The research was conducted on five informants and varying levels of education. As for the family functions that can be carried out by early married couples, almost all of them can be carried out, such as; religious function, affection function, reproductive function, education and socialization function, economic function, recreation function, protection function, and environmental development function, although in limited cases. Meanwhile, the obstacles faced by early married couples in carrying out family functions, such as lack of financial independence, and interaction problems.

Cooperative Behavior of Prosumers in Integrated Energy Systems

The technical complexity of organizing energy systems’ operation has recently been compounded by the complexity of reconciling the interests of individual entities involved in interactions. This study proposes a possible solution to the problem of modeling their relationships within a large system. Our solution takes into account multiple levels of interactions, imperfect information, and conflicting interests. We present a mathematical statement of the problem of optimal interactions between the centralized system and prosumers in the integrated energy system (IES) with due consideration of the layered architecture of the IES. The paper also contributes a model for arranging the interactions between centralized and distributed energy sources for cases when IES prosumers form coalitions. The implementation of this model is based on multi-agent techniques and cooperative game theory tools. In order to arrive at a rational arrangement of the interactions of prosumers in the IES, the model implements different approaches to the allocation of the coalition’s total payoff (the Shapley value, Modiclus, PreNucleolus solution concepts). Furthermore, we propose a criterion for deciding on the “best” imputation. We contribute a multi-agent system that implements the proposed model and use a test IES setup to validate the model by simulations. The results of the simulations ensure optimal interactions between the entities involved in the energy supply process within the IES and driven by their own interests. The results also elucidate the conditions that make it feasible for prosumers to form coalitions.

General Spin-Restricted Open-Shell Configuration Interaction Approach: Application to Metal K-Edge X-ray Absorption Spectra of Ferro- and Antiferromagnetically Coupled Dimers.

In this work, we present a generalized implementation of the previously developed restricted open-shell configuration interaction singles (ROCIS) family of methods. The new method allows us to treat high-spin (HS) ferro- as well as antiferromagnetically (AF) coupled systems while retaining the total spin as a good quantum number. To achieve this important and nontrivial goal, we employ the machinery of the iterative configuration expansion (ICE) method, which is able to tackle general configuration interaction (CI) problems on the basis of spin-adapted configuration state functions (CSFs). While ICE is designed to work in restricted orbital spaces, the new general-spin ROCIS (GS-ROCIS) method is designed to be applicable to larger molecules by employing a prototyping strategy. This new method can be applied to closed-shell, high-spin open-shell, as well as antiferromagnetic reference CSFs. In addition, GS-ROCIS can be combined with the pair natural orbital (PNO) machinery in the form of the PNO-GS-ROCIS method. With this extension, one can drastically reduce the required virtual space in the vicinity of the involved core orbitals, leading to computational savings of several orders of magnitude with negligible (<1%) loss in accuracy. To demonstrate the use of the new methodology, the metal K pre-edge X-ray absorption excitation problem of an antiferromagnetically coupled copper model dimer was investigated. By first analyzing a model copper dimer, it is shown that even for the minimum core excitation problem that involves the two antiferromagnetically coupled singly occupied orbitals and one virtual orbital, the resulting GS-ROCIS and broken-symmetry configuration interaction singles (BS-CIS) spectra may differ in terms of the number, energy position, and relative intensity of the computed bands. Furthermore, the methodology was validated to perform equally well in computing the K-edge spectra of antiferromagnetic nickel oxide dimers and mixed-valence cobalt oxide trimers. Collectively, the present development represents an important methodological advance in the application of theoretical X-ray spectroscopy.

CALCULATION OF STATIC DEFORMATION OF AXISYMMETRIC SHELLS OF ROTATION WITH DIFFERENTIAL MODEL

In the paper differential equations of static geometrically nonlinear deformation of axisymmetric shell of rotation are obtained. The resolving functions are projections of vectors in the global coordinate system. The equations allow describing any geometry of meridian (breaks, curvature jumps), large deformations, changing of shell thicknesses during deformation, also cross shears characteristic for thick shells. For the numerical solution, the approach based on the finite difference method is applied, which is realized in the own software package for the calculation of the mechanics of spatial rod systems – DARSYS. The calculations of test problems of the internal pressure inflation of cylindrical, spherical, elliptical, conical shells, as well as a combined conicalcylindrical shell with a meridian break are presented. Graphs of convergence of displacements at the reference points as a function of mesh density and under load variation are given, and deformed meridian configurations are plotted. The solutions obtained in ANSYS by different finite elements of Shell type were used as a reference for comparison. APDL scripts for parametric calculations of the test problems are given in the text of the paper. The proposed approach to the calculation of static deformation of shells of rotation has shown good agreement with finite element modeling in ANSYS (including thick shells) and in the future will be extended to the modeling of dynamic deformation and the possibility of solving coupled problems of interaction with liquid or gas. The given equations of the axisymmetric shell are a special case of the general equations, the development and application of which are beyond the scope of this paper, and the obtained solution results are the first stage of testing the developed complex approach to the calculation of static and dynamic deformation of shells, alternative to finite-element modeling.

MODELING THE DEFORMATION PROCESS OF AN UNDERWATER GAS PIPELINE UNDER THE EXPLOSIVE LOADING

The process of deformation of an underwater two-layer gas pipeline during the explosion of a nearby octogen charge is simulated. For modeling, a specially developed proprietary software package is used to solve three-dimensional dynamic problems of interaction of elastoplastic structures with compressible media, based on a single Godunov scheme of increased accuracy for calculating the joint motion of gas, liquid, and elastoplastic media. The package uses an Eulerian-Lagrangian approach with explicit identification of moving contact surfaces between different media. For each environment, three types of computational grids are used. These are Lagrangian surface meshes in the form of a continuous set of triangles for specifying the initial geometry of bodies and accompanying them during the calculation process, as well as two types of three-dimensional volumetric meshes automatically generated during the calculation process. The charge, which has a spherical shape, is initiated at its center. To describe the process of propagation of steady-state detonation, the hydrodynamic theory of detonation is used. Shock waves generated during an explosion in the surrounding liquid interact with a fragment of a two-layer pipeline and a solid bottom. Wave processes are analyzed both in the steel pipe and in the concrete shell that weighs it down. Loads on the pipeline are estimated depending on the distance to the charge and the position of the pipeline relative to the bottom. The possible destruction of both steel and concrete weight shells in areas of tensile deformations that are formed in places of the maximum bending of the pipeline is shown. It is shown that the proximity of the bottom can significantly enhance the impact of explosive loading due to the action of shock waves reflected from the bottom.

ТИПЫ ОБЩНОСТЕЙ КУЛЬТУР НАРОДОВ ЮЖНОГО УРАЛА И ПРИУРАЛЬЯ В СВЕТЕ КОНЦЕПЦИИ Р.Г. КУЗЕЕВА

The materials of this publication were announced at the International Scientific and Practical Conference "Ethnos. Society. Civilization: VII Kuzeev Readings" (Ufa, September 26–27, 2024), dedicated to the 95th anni- versary of the outstanding ethnographer, ethnologist, organizer of science, public figure Rail Gumerovich Kuzeev. It is shown, that the scientific problem of intercultural interactions and mutual influences was formulated by R.G. Kuzeev as particularly relevant for a multiethnic region and was developed at the Institute of Ethnological Research of the UFIC RAS, which now bears his name, for many years. The possibility of its development associ- ated with the nomination by R.G. Kuzeev of the theory of the formation of the Volga-Ural historical and ethnolog- ical region, the organization of regional ethnographic science, the training of R.G. Kuzeev and his associates of scientific personnel – specialists in the field of ethnography and folklore of Turkic, East Slavic, Finno–Ugric and other peoples, conducting systematic field research in various fields ethnic cultures. The author of the publication, based on the theory and methodology of the WG. Kuzeeva characterizes the commonality of the cultures of the peoples of the Southern Urals and the Urals, which arose as result of the formation within the framework of one ethnogenetic core, and subsequently long-term ethnic interactions and mutual influences. The result of the study was the identification of a syncretic and synthetic ethnocultural community of Russians, Bashkirs, Tatars, Chu- vash, Udmurts, Mari, Ukrainians, Belarusians, Latvians, Kryashens. The musical folklore of the Chuvash and Udmurts shows the influence of Bashkirs and Tatars on the development of melodic ornamentation and pentatonics, as well as the formation of a Russian ethnocultural superstrate in the region. The ritual culture pro- vides examples of the perception of Bashkir and Tatar customs by the Chuvash, Mari and Udmurts (sapantuy among the Chuvash, diyyn among the Mari, ӟаӟег ыш among the Udmurts), and in recent years – the unification of many national holidays and rituals. The economic activity emphasizes the role of the Russian peasant popula- tion as an intermediary in the transfer of traditions from Western immigrants (Latvians, Ukrainians, Belarusians) to local ethnic groups. In the anthroponymy of peoples, general patterns established due to socio-economic pro- cesses and the prevailing ideology (names-Sovietism, international words) and the perception by some immi- grants, for example, Udmurts, of Turkic names that have become ethnically traditional.

Parental Views and Experiences on the Instruction of Safety Skills to Children with ASD

Introduction: The problems in social interaction and communication, limited interest, and repetitive behavior observed in children with autism spectrum disorder (ASD) increase the vulnerability of these children to security risks. Research demonstrated that children with ASD are more vulnerable to security risks when compared to children with typical development. The present study aimed to determine the views and experiences of parents of children with ASD on safety skills and instruction of these skills. Method: The study was designed with the descriptive model. Participants were assigned with the criterion sampling, maximum variation sampling, and convenience sampling methods. The study data were collected from 43 parents in semi-structured interviews and analyzed with the descriptive approach. Findings: More than half of the participants described safety skills as learning the skills that would protect the child, and they previously experienced situations that threatened the safety of their children, and they had taken precautions to ensure the safety of their children by reducing the exposure of their children to dangerous situations or increasing surveillance. A significant number of the participants stated that safety skills could be instructed, while nearly half stated that the children were not instructed safety skills at school. Most participants stated that they had experience in the instruction of safety skills, they usually instructed these verbally or by warning their children, albeit the instruction was challenging. Discussion: It was observed that parents' knowledge, teaching experience, and views on the definition and scope of safety skills were limited. The study findings were generally consistent with the findings reported in the literature. Conclusion: The findings demonstrated that parents did not prioritize the instruction of safety skills and did not assist their children in safe responses and self-protection. The awareness, knowledge, and teaching skills of parents of children with ASD should be improved in terms of safety skills.

Study on the ice-water interaction problem based on MPS-NDEM coupling model

Ice-water coupling is a unique fluid-solid interaction problem characterized by collisions and hydrodynamic interaction between multiple bodies, accompanied by significant changes in the free surface. This paper presents a novel numerical model that achieves two-way coupling between the moving particle semi-implicit (MPS) method and the non-smooth discrete element method (NDEM) to simulate ice-water interactions. The MPS method is employed to model fluid motion, while the NDEM is applied to simulate the motion and collision of ice floes. The improved MPS method presented in this study, based on our previous research, addresses several issues found in the traditional MPS method. To improve the computational efficiency, the domain decomposition method is implemented to parallel the fluid solver and the AMG preconditioned GMRES iterative solver is selected as the optimal solution scheme for the improved MPS method. The accuracy and feasibility of the present coupling model are validated through benchmark cases, such as dam break, wave motion, ice motion in regular waves and debris dam break flow. Furthermore, the simulation of the ship moving in the broken ice field is successfully conducted with the coupling model and the influence of ice-water coupling load on predicting broken ice resistance is also investigated.

On an immersed boundary technique for modeling 3D incompressible fluids laden with particles

This work presents results from a recently developed three-dimensional immersed boundary technique for modeling 3D particle-laden fluid problems. A classical Eulerian approach is followed to describe the fluid (assumed here as incompressible through Navier-Stokes equations). A discrete element formulation, in turn, is used to describe the particles´ dynamics. The fluid-particle interfaces are treated through Nitsche’s method, which is an immersed boundary technique whereby we impose the particles´ surface velocities and spins as boundary conditions to the fluid in a weak form. Here, particle-to-wall (i.e., fluid´s exterior solid boundaries) contacts are fully permitted and resolved. In order to assess the accuracy and efficiency of the developed scheme, numerical simulations of 3D unsteady flow of an incompressible fluid loaded with particles are performed and compared against benchmark solutions. This work refers to an intermediate stage of a scientific research that aims to model problems of fluid-particle interaction (FPI) with full particle-to-particle contacts in particle-laden fluids.

Analysis of the fluid-structure interaction of a 2D model of the savonius rotor, using immersed boundary and fourier pseudospectral methods

Savonius rotors are a unique type of vertical axis wind turbine (VAWT) characterized by its “S” shape, with low rotational speed, low noise and good automatic start-up capability. This turbine has a great profile forsmall businesses and residences. The present work presents a simplified modeling of the fluid-structure interaction problem of a Savonius rotor, using the Fourier pseudospectral method (FPSM) coupled to the immersed bound-ary method (IBM), considering the Newtonian fluid, incompressible flow, without heat transfer and gravitational effects, with constant and two-dimensional (2D) properties. The results presented address the flow over a freely rotating vertical turbine, which allows the analysis of the evolution of the moment coefficient (Cm ) in relation to temporal evolution, azimuthal position (&amp;#952;) and the blade tip speed ratio (&amp;#955;).

Boundary element method for hypersingular integral equations: Implementation and applications in potential theory

The main objective of this paper is to develop effective numerical methods to solve hypersingular integral equations arising in various physical and mechanical applications. Both surface and contour integrals are considered. The novelty of the proposed approach lies in the exact formulas obtained for an arbitrary planar polygon in hypersingular integral estimations. A one-dimensional hypersingular integral equation is derived for axially symmetrical configurations, and analytical formulas are established for calculating the hypersingular parts. It is proved that the hypersingular component of the surface integral is equal to its hypersingular component along the tangent plane. These exact formulas enable the development of an effective numerical method based on boundary element implementation. Benchmark tests are considered, and the convergence of the proposed methods is demonstrated. Problems in crack analysis are formulated and solved using both surface and contour hypersingular integral equations. A comparison of the results is made between boundary element methods and finite element methods for penny-shaped cracks. Boundary value problems in fluid-structure interaction are considered, and numerical simulations are performed. An estimation of modes and frequencies of panel and blade vibrations when interacting with liquids is carried out.