Habaršy. Fizika-matematikalyķ ġylymdary seriâsy

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1728-7901

2959-5886

2959-5894

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Mathematics Education...

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РЕШЕНИЕ НЕЛИНЕЙНОЙ СТАЦИОНАРНОЙ ЗАДАЧИ БАРОКЛИННОГО ОКЕАНА МЕТОДОМ ФИКТИВНЫХ ОБЛАСТЕЙ
(2024-01-24)
O.S. Akhmetova
;
S.A. Issayev
;
A.N. Kaziyeva
Modeling is a key tool for understanding physical processes, analyzing the global spatial and temporal structure of the ocean, its interaction with the atmosphere, and regional variability in marine and ocean systems. Models also play an important role in processing and assimilating data from field observations. The development of mathematical modeling of ocean dynamics, which has more than a century of experience, has led to a significant increase in understanding of the physical processes occurring in the marine environment, as well as improved methods and models for their analysis. In addition, in recent years there has been increasing interest in studying the patterns of baroclinic fields, disturbances, and anomalies inthe ocean, including the analysis of observational data, theoretical studies of the propagation of disturbances in a simplified oceanic environment, and numerical modeling. The basic principles of the theory of the baroclinic layer in the ocean can be derived from a complete set of primitive equations, including horizontal projections of the momentum balance equations, the hydrostatic equation, the mass conservation equation, the heat and salt diffusion equations, and the equation of state.This article discusses the fictitious domain method for the nonlinear stationary problem of the Baroclinic Ocean. A generalized solution to the problem is given and its uniqueness is proved. The theorem of existence and convergence of solutions to approximate models obtained using the fictitious domain method are studied. Моделирование является ключевым инструментом для осмысления физических процессов, анализа всемирной пространственно-временной структуры океана, его взаимодействия с атмосферой и региональной изменчивости морских и океанических систем. Модели также играют важную роль в обработке и ассимиляции данных из натурных наблюдений. Развитие математического моделирования динамикиокеана, имеющего более чем столетний опыт, привело к значительному углублению понимания физических процессов, происходящих в морской среде, а также к улучшению методов и моделей их анализа. Помимо этого, в последние годы усиливается интерес к исследованиюзакономерностей бароклинных полей, возмущений и аномалий в океане, включая анализ данных наблюдений, теоретическое исследование распространения возмущений в упрощенной океанической среде и численное моделирование. Основные принципы теории бароклинного слоя в океане могут быть выведены из полного набора примитивных уравнений, включающих горизонтальные проекции уравнений баланса количества движения, уравнение гидростатики, уравнение сохранения массы, уравнения диффузии тепла и соли, а также уравнение состояния.В данной статье рассматривается метод фиктивных областей для нелинейной стационарной задачи бароклинного океана. Дается обобщенное решение задачи и доказывается его единственность. Исследованы теорема существования и сходимости решения приближенных моделей, полученных с помощью метода фиктивных областей. Модельдеу физикалық процестерді түсінудің, мұхиттың ғаламдық кеңістіктік және уақыттық құрылымын, оның атмосферамен әрекеттесуін және теңіз және мұхит жүйелеріндегі аймақтық өзгермелілігінталдаудыңнегізгі құралы болып табылады. Модельдер далалық бақылаулардан алынған деректерді өңдеу мен ассимиляциялауда да маңызды рөл атқарады. Ғасырдан астам тәжірибесі бар мұхит динамикасын математикалық модельдеудің дамуы теңіз ортасында болып жатқан физикалық процестерді түсінудің айтарлықтай артуына, сондай-ақ оларды талдаудың әдістері мен үлгілерінің жетілдірілуіне әкелді. Сонымен қатар, соңғы жылдары мұхиттағы бароклинді өрістердің заңдылықтарын, бұзылулар мен аномалияларды зерттеуге, соның ішінде бақылау деректерін талдауға, жеңілдетілген мұхиттық ортада бұзылулардың таралуын теориялық зерттеуге және сандық модельдеуге қызығушылық артуда. Мұхиттағы бароклинді қабат теориясының негізгі принциптері импульс тепе-теңдік теңдеулерінің горизонталь проекцияларын, гидростатикалық теңдеулерді, массаның сақталу теңдеулерін, жылу мен тұздардың диффузия теңдеулерін қоса алғанда, қарабайыр теңдеулердің толық жиынтығынан алынуы мүмкін. күй теңдеуі.Бұл мақалада бароклинді мұхиттың сызықты емес стационарлық мәселесі үшін жалғандомен әдісі талқыланады. Мәселенің жалпыланған шешімі келтіріліп, оның бірегейлігі дәлелденеді. Жалған домен әдісі арқылы алынған жуықталған модельдерге шешімдердің бар болуы және жинақтылығы теоремасы зерттеледі.
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REPRESENTATION OF A NON-STATIONARY MODEL OF BAROCLINIC OCEAN MOTION USING THE FICTITIOUS DOMAIN METHOD
(2024-06-01)
O.S. Akhmetova
;
Ye.V. Morozova
;
S.A. Issayev
This paper presents a groundbreaking non-stationary model, intricately crafted using the fictitious domain technique, to delve into the complex dynamics of baroclinic ocean motion. This study marks a significant leap in our understanding of water mass interaction, shedding light on the profound impact of temperature and salt gradients on sea currents.The methodology uses modified Navier-Stokes equations for viscous, incompressible flow, considering advection, diffusion, and Coriolis force.The results of this study underscore the immediate and tangible implications of our research. The solutions unveiled the pivotal role of pressure and temperature differentiation in the genesis of ocean currents. The analysis demonstrated that by integrating nonlinear terms and detailed modeling of initial and boundary conditions, we can markedly improve the precision of water mass movement forecasts. This work underscores the urgent necessity for further research into dynamic ocean modeling to enhance our ability to predict climate change.This article introduces truly innovative approaches to numerical modeling, which hold immense potential for the future of the field. These approaches have the power to transform existing models of sea currents and pave the way for the development of more efficient methods for monitoring and predicting the state of the marine environment.
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PROSPECTS AND POSSIBLE RISKS OF THE APPLICATION OF SMART CONTRACTS IN SCIENCE AND EDUCATION
(2020-09-29)
O.S. Akhmetova
;
S.A. Issayev
Important advantages of the potential use of blockchain in the scientific and educational field are security, immutability, transparency. By providing a framework for decentralized forms of government and smart contracts, while significantly reducing the potential for fraudulent and corrupt practices, this technology can help safeguard public interests and state sovereignty. Today, attempts are being made to develop various technological solutions based on blockchain for various areas of social interaction. One example is the drafting of smart contracts aimed at solving a number of tasks in scientific and educational activities. The article discusses the possibilities and prospects of using blockchain technology and smart contracts in science and education. The topic causes controversy among specialists: some are convinced of the effectiveness of the proposed solutions, while others point to the negative consequences and obstacles to the introduction of new technology. The authors analyzed possible ways of introducing blockchain technology and smart contracts in the field of education and science, as well as the possible risks associated with their use.
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STATIONARY DIFFUSION MODEL IN HETEROGENEOUS MEDIA WITH SMALL PARAMETERS
(2025-06-01)
O.S. Akhmetova
;
S.A. Issayev
This study presents a theoretical and applied investigation of a stationary diffusion problem in heterogeneous media incorporating small parameters and modified boundary conditions. The relevance of this work stems from the necessity to accurately represent boundary layer effects in complex physical systems with variable internal structures, such as multilayered materials, biological tissues, and natural geophysical environments. Traditional models often oversimplify such effects, resulting in distortions in the solution near domain boundaries.The primary objective of the research is to construct a rigorous mathematical framework that accounts for both the presence of small parameters and altered boundary conditions. The analysis includes deriving a priori stability estimates and constructing asymptotic expansions for the solution. The methodology relies on functional formulation in Sobolev spaces, the Galerkin method, asymptotic techniques, and weak convergence theory. Special attention is given to the existence and uniqueness of both strong and generalized solutions, as well as to their convergence properties as the small parameters tend to zero.The results confirm the solvability of the problem, provide robust energy estimates, and establish solution stability under various types of boundary modifications. It is demonstrated that changes in boundary conditions primarily affect solution behavior near the domain edges, while preserving the global structure of the field. The model is applied in various fields, including climate modeling, thermal diffusion, and hydrophysical systems. This work lays a foundation for the development of adaptive numerical schemes and for extending the analysis to non-stationary problems.
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APPLICATION OF THE FICTITIOUS REGION METHOD TO SOLVING A MODEL OCEANOLOGY PROBLEM
(2023-09-01)
O.S. Akhmetova
;
S.A. Issayev
The study of the laws of fluid motion has always been an important aspect of the development of both technical and natural sciences. The solution to various problems arising in the analysis of fluid dynamics can be carried out both at the theoretical level and through carefully designed physical experiments. However, in many cases, creating models to study fluid phenomena is challenging, especially in laboratory or field studies. Physical experiments aimed at the detailedstudy of fluid motion often encounter technical difficulties and require significant resources and financial costs. In addition, the data obtained from such experiments are often limited in their applicability.This is why mathematical modeling plays a significant role in research in fluid dynamics. This makes it possible to more efficiently and cheaply study various aspects of fluid motion, and also provides the opportunity to apply the results obtained more widely. Modeling allows you to consider variousfactors affecting fluid movement and analyze their impact on the final result. Thus, mathematical modeling becomes an important tool for understanding and improving fluid movement concepts in various science and technology fields.This article discusses the fictitious domain method for a linear ocean flow problem. A generalized solution to the problem is given and its uniqueness is proved. The theorem of existence and convergence of solutions to approximate models obtained using the fictitious domain method are studied.
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FORMATION FUTURE COMPUTER SCIENCE TEACHERS’ COMMUNICATIVE ABILITIES IN STUDYING INTERNET OF THINGS (IoT)
(2020-09-29)
O.S. Akhmetova
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S.A. Issayev
;
A.K. Kaiyrgaliyeva
To date, several trends in digital technologies have been identified, among which the Internet of Things stands out – a network of digital devices and devices that interact via the Internet. The application areas of the Internet of Things are very wide: industrial technologies, remote service and survival technologies, educational technologies. Modern digital technologies should be introduced into the content of technological education in schools and in the training of computer science teachers. This need is also determined by the currently implemented national projects "Digital Kazakhstan" and "Education". The purpose of the article is to consider the Internet of Things as the content of technological education of future computer science teachers. The article will focus on the formation and development of professional ICT (information and communication technologies) qualifications of the future computer science teacher when teaching the Internet of Things in higher education institutions. When teaching the Internet of Things (IoT), the problems that may arise are taken into account, and it is described how this affects the information and communication skills of the future teacher.
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Habaršy. Fizika-matematikalyķ ġylymdary seriâsy

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