Нестаціонарні теплові процеси в анізотропних твердих тілах

Дисертацію присвячено дослідженню теплових процесів в анізотропних твердих тілах за допомогою безсіткового методу розв’язання тривимірних задач нестаціонарної теплопровідності. Серед великого розмаїття задач математичної фізики, які нині успішно вирішуються, особливу роль займають задачі теплопровідності в анізотропних матеріалах. Насамперед це пов’язано з активним використанням анізотропних матеріалів при виготовленні великої кількості сучасних приладів та пристроїв, деталей конструкцій та машин – наприклад, трансформаторів із сердечниками з текстурованої сталі (в електротехніці), лопаток газотурбінних двигунів із жароміцних нікелевих сплавів з монокристалічною структурою (в авіації), п’єзоперетворювачів, електрооптичних модуляторів та рідкокристалічних індикаторів (в електронному приладобудуванні). Сучасні анізотропні матеріали зі складною структурою (наприклад, композитні матеріали, багатошарові матеріали, покриття, нанесені на підкладки) все частіше використовуються в новітніх інженерних розробках, а також в якості конструкційних матеріалів.У різних технологічних процесах і пристроях дані матеріали піддаються тепловому впливу, внаслідок чого в них відбуваються фізико-хімічні явища, зокрема зміна геометричних розмірів. Неконтрольоване теплове розширення конструкційних матеріалів може призвести до погіршення експлуатаційних характеристик пристрою, а також до аварійних ситуацій. Тому при створенні та використанні таких матеріалів необхідно враховувати анізотропію їх теплофізичних властивостей, а також досліджувати теплові процеси, які в них протікають. The dissertation deals with the study of thermal processes in anisotropic solids by meshless method for solving three-dimensional non-stationary heat conduction problems. Heat conduction problems in anisotropic solids play a significant role among the wide variety of problems of mathematical physics which are currently being successfully solved. First of all, it is associated with the active use of anisotropic materials in the manufacture of a large number of modern instruments and devices, structural parts and machines. For example, transformers with textured steel cores (in electrical engineering), gas-turbine engine blades of heat-resistant nickel alloys with a single-crystal structure (in aviation), piezoelectric transducers, electro-optic modulators and liquid crystal indicators (in electronic instrument engineering). Modern anisotropic materials with a complex structure (composite materials, multilayered materials, coatings on substrates, etc.) are increasingly used in advanced engineering designs and as structural materials. In various technological processes and devices, these materials are exposed to thermal effects, resulting in physical and chemical phenomena, including changes in geometric parameters. Uncontrolled thermal expansion of structural materials may lead to device performance degradation, as well as to emergency situations. Therefore, when creating and using such materials, it is necessary to take into account the anisotropy of their thermophysical properties, as well as to study the thermal processes occurring in them

Applied Mathematics and Computational Physics

As faster and more efficient numerical algorithms become available, the understanding of the physics and the mathematical foundation behind these new methods will play an increasingly important role. This Special Issue provides a platform for researchers from both academia and industry to present their novel computational methods that have engineering and physics applications

Vision 2040: A Roadmap for Integrated, Multiscale Modeling and Simulation of Materials and Systems

Over the last few decades, advances in high-performance computing, new materials characterization methods, and, more recently, an emphasis on integrated computational materials engineering (ICME) and additive manufacturing have been a catalyst for multiscale modeling and simulation-based design of materials and structures in the aerospace industry. While these advances have driven significant progress in the development of aerospace components and systems, that progress has been limited by persistent technology and infrastructure challenges that must be overcome to realize the full potential of integrated materials and systems design and simulation modeling throughout the supply chain. As a result, NASA's Transformational Tools and Technology (TTT) Project sponsored a study (performed by a diverse team led by Pratt & Whitney) to define the potential 25-year future state required for integrated multiscale modeling of materials and systems (e.g., load-bearing structures) to accelerate the pace and reduce the expense of innovation in future aerospace and aeronautical systems. This report describes the findings of this 2040 Vision study (e.g., the 2040 vision state; the required interdependent core technical work areas, Key Element (KE); identified gaps and actions to close those gaps; and major recommendations) which constitutes a community consensus document as it is a result of over 450 professionals input obtain via: 1) four society workshops (AIAA, NAFEMS, and two TMS), 2) community-wide survey, and 3) the establishment of 9 expert panels (one per KE) consisting on average of 10 non-team members from academia, government and industry to review, update content, and prioritize gaps and actions. The study envisions the development of a cyber-physical-social ecosystem comprised of experimentally verified and validated computational models, tools, and techniques, along with the associated digital tapestry, that impacts the entire supply chain to enable cost-effective, rapid, and revolutionary design of fit-for-purpose materials, components, and systems. Although the vision focused on aeronautics and space applications, it is believed that other engineering communities (e.g., automotive, biomedical, etc.) can benefit as well from the proposed framework with only minor modifications. Finally, it is TTT's hope and desire that this vision provides the strategic guidance to both public and private research and development decision makers to make the proposed 2040 vision state a reality and thereby provide a significant advancement in the United States global competitiveness

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal